NASA CR-168031

GARSETT 21-4302

DILUTIONJET MIXINGPROGRAM

PHASEI REPORT

by

R. SRINIVASAN

A. BERENFELD

H,C.MONGIA

GarrettTurbine EngineCompany

A Oivision of the Garrett Corporation

November 1982

Prepared for

NationalAeronauticsand SpaceAdministration

NASA-LewisResearchCenter

Contract NAS3-22110
TABLE OF CONTENTS

1.0

2.0

3.0

4.0

5.0

6.0

7.0

SUMMARY

INTRODUCTION AND OBJECTIVES

TEST RIG AND FACILITY DESCRIPTIONS

3.1 Test Rig

3.1.1 Profile Generator

3.1.2 Test Sections

3.1.3 Dilution Orifice Plate Geometry

3.2 Test Facilities

DATA ACQUISITION AND REDUCTION

4.1 Data Acquisition

4.2 Data Reduction

EXPERIMENTAL DATA

5.1 Series 1 Tests

5.1.1 Conclusions for Series 1 Tests

5.2 Series 2 Tests

5.2.1 Conclusions for Series 2 Tests

5.3 Series 3 Tests

5.3.1 Symmetric Convergence Test Sections

5.3.2 Asymmetric Convergence Test Sections

5.3.3 Conclusions for Series 3 Tests

5.4 Series 4 Tests

5.4.1 Conclusions for Series 4 Tests

JET MIXING CORRELATIONS DEVELOPMENT

6.1 NASA/Aerojet Correlations

CONCLUSIONS AND RECOMMENDATIONS

APPENDIXES

A Symbols

B References

DISTRIBUTION LIST

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LIST OF ILLUSTRATIONS

Title

Multiple Jet Study Coordinate System and

Important Nomenclature

Jet Mixing Rig Schematic

Partially Assembled Dilution Jet Mixing

Test Rig

Profile Generator

Jet Mixing Test Sections

Test Section Wall Statics and Thermocouples

Dilution Orifice Plate Configurations

Total Pressure, Thermocouple, and Static

Pressure Rake

X-Y-Z Actuator with the Rake Mounted

jet Mixing Rig as Viewed from

Rig Discharge End

Typical Comparison Between Data from

NASA/Aerojet and Present Investigation

Measured Theta Distributions for Test No. 1

with Tm = Constant, J = 5.74, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 1

with Tm = Constant, J = 5.74, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 2

with Tm = Constant, J= 21.59, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 2

with Tm = Constant, J = 21.59, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 3

with Tm = Constant, J = 6.14, S/D = 4,

and Ho/D = 4.

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Figure

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LIST OF ILLUSTRATIONS (CONTD)

Title

Predicted Theta Distributions for Test No. 3

wlth Tm = Constant, J= 6.14, S/D = 4,

and Ho/D = 4.

Measured Theta Distributions for Test No. 4

wlth T m = Constant, J = 26.7, S/D = 4,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 4

with T m = Constant, J = 26.7, S/D -- 4,

and Ho/D = 4.

Measured Theta Distributions for Test No. 5

wlth T m = Constant, J = 25.32, S/D = 2,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 5

with T m = Constant, J = 25.32, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 6

with T m -- Constant, J = 107.8, S/D = 2,

Ho/D = 8.

Predicted Theta Distributions for Test No. 6

wlth T m = Constant, J = 107.8, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 7

wlth T m = Constant, J = 26.3, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 7

wlth T m = Constant, J = 26.3, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 8

wlth T m = Constant, J = 109.0, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 8

wlth T m = Constant, J = 109.0, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 9

wlth Hot Jets, J = 31.0, S/D = 2,

and Ho/D = 4.

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LIST OF ILLUSTRATIONS (CONTD)

Title

Predicted Theta Distributions for Test No. 9

with Hot Jets, J = 31.0, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 10

with Hot Jets, J = 30.64, S/D = 4,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 10

wlth Hot Jets, J = 30.64, S/D = 4,

and Ho/D = 4.

Measured Theta Distributions for Test No. iI

wlth Hot Jets, J = 30.19, S/D = 2,

and Ho/D = 8.

Predicted Theta Distributions for Test No. ii

with Hot Jets, J = 30.19, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 12

with Hot Jets, J = 30.53, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 12

with Hot Jets, J = 30.53, S/D = 4,

and Ho/D = 8.

Profiled Mainstream Theta Distributions used

in Series 2 Tests.

Measured Theta Distributions for Test No. 13

with Top Cold Profile, J = 22.63, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 13

with Top Cold Profile, J = 22.63, S/D = 2,

and Ho/D = 4

Measured Theta Distributions for Test No. 14

with Top Cold Profile, J = 7.5, S/D = 4,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 14

with Top Cold Profile, J = 7.5, S/D = 4,

and Ho/D = 4.

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Figure

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LIST OF ILLUSTRATIONS (CONTD)

Title

Measured Theta Distributions for Test No. 15

wlth Top Cold Profile, J = 109.9, S/D = 2,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 15

with Top Cold Profile, J = 109.9, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 16

with Top Cold Profile, J = 22.55, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 16

with Top Cold Profile, J = 22.55, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 17

with Top Hot Profile, J = 22.14, S/D = 2,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 17

with Top Hot Profile, J = 22.14, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 18

with Top Hot Profile, J = 27.69, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 18

with Top Hot Profile, J = 27.69, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 19

with Test Section II, J = 27.09, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 19

with Test Section II, J = 27.09, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 20

wlth Test Section II, J = 102.5, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 20

wlth Test Section II, J = 102.5, S/D = 4,

and Ho/D = 8.

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LIST OF ILLUSTRATIONS (CONTD)

Title

Measured Theta Distributions for Test No. 21

with Test Section II, J = 6.76, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 21

with Test Section II, J = 6.76, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 22

with Test Section II, J = 26.07, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 22

with Test Section II, J = 26.07, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 23

with Test Section IV, J = 21.07, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 23

with Test Section IV, J = 21.07, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 24

with Test Section IV, J = 85.84, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 24

with Test Section IV, J = 85.84, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 25

with Test Section IV, J = 6.73, S/D = 4,

and Ho/D = 8

Predicted Theta Distributions for Test No. 25

wlth Test Section IV, J = 6.73, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 26

with Test Section IV, J = 26.73, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 26

wlth Test Section IV, J = 26.73, S/D = 2,

and Ho/D = 4.

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LIST OF ILLUSTRATIONS (CONTD)

Title

Measured Theta Distributions for Test No. 27

with Test Section V, J = 27.13, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 27

with Test Section V, J = 27.13, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 28

with Test Section V, J = 106.7, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 28

with Test Section V, J = 106.7, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 29

with Test Section V, J = 7.07, S/D = 2,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 29

with Test Section V, J = 7.07, S/D = 2,

and Ho/D = 8.

Measured Theta Distributions for Test No. 30

with Test Section V, J = 27.31, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 30

with Test Section V, J = 27.31, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 31

with Test Section VI, J = 26.59, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 31

with Test Section VI, J = 26.59, S/D = 4,

and Ho/D = 8.

Measured Theta Distributions for Test No. 32

with Test Section VI, J = 107.8, S/D = 4,

and Ho/D = 8.

Predicted Theta Distributions for Test No. 32

with Test Section VI, J = 107.8, S/D = 4,

and Ho/D = 8.

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LIST OF ILLUSTRATIONS (CONTD)

Title

Measured Theta Distributions for Test No. 33

with Test Section VI, J = 7.05, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 34

with Test Section VI, J = 7.05, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 34

wlth Test Section VI, J = 26.4, S/D = 2,

and Ho/D = 4.

Predicted Theta Distributions for Test No. 34

wlth Test Section VI, J = 26.4, S/D = 2,

and Ho/D = 4.

Measured Theta Distributions for Test No. 35

with Top Cold Profile, Test Section V,

J = 26.82, S/D = 4, and Ho/D = 8.

Predicted Theta Distributions for Test No. 35

with Top Cold Profile, Test Section V,

J = 26.82, S/D = 4, and Ho/D = 8.

Measured Theta Distributions for Test No. 36

with Top Cold Profile, Test Section V,

J = 109.8, S/D = 4, and Ho/D = 8.

Predicted Theta Distributions for Test No. 36

wlth Top Cold Profile, Test Section V,

J = 109.8, S/D = 4, and Ho/D = 8.

Measured Theta Distributions for Test No. 37

with Top Hot Profile, Test Section V,

J = 8.51, S/D = 4, and Ho/D = 8.

Predicted Theta Distributions for Test No. 37

with Top Hot Profile, Test Section V,

J = 8.51, S/D = 4, and Ho/D = 8.

Measured Theta Dis£ributions for Test No. 38

with Top Hot Profile, Test Section V,

J = 30.24, S/D = 4, and Ho/D = 8.

Predicted Theta Distributions for Test No. 38

with Top Hot Profile, Test Section V,

J = 30.24, S/D = 4, and Ho/D = 8.

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Table

I

II

III

IV

V

VI

LIST OF TABLES

Title

Definition of Test Sections

Description of Dilution Orifice Plates

Series 1 Test Configurations and Flow

Conditions

Series 2 Test Configurations and Flow

Conditions

Series 3 Test Configurations and Flow

Conditions

Series 4 Test Configurations and Flow

Conditions

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1.0 SUMMARY

The main objective of the NASA Dilution Jet Mixing Phase I

Program was to quantify by means of parametric tests the effect of

the following on the mixing of a row of jets with a confined crossflow.

o Jet to mainstream density ratio

o Flow area convergence as encountered in transition sections

o Non-uniform mainstream profile upstream of dilution

orifices.

The general conclusions derived from Phase I work are:

o Jet spreading rate in transverse direction is increased

with increasing J, H/D and with decreasing S/D.

o The density ratio has only a second order effect on the

jet mixing characteristics for a constant momentum

ratio.

o The temperature distributions in the jet mixing region

are strongly influenced by the undisturbed mainstream

profile. Therefore, a superposition of the mainstream

profile on the correlations for isothermal mainstream

conditions yields good agreement with data.

o Flow area convergence enhances mixing in radial and

transverse directions. An asymmetric convergent duct

with flat wall injection has the same jet mixing characteristics as a symmetric convergent duct. An asymmetric

convergent duct with slant wall injection has a faster

jet spreading rate in the transverse direction.
2.0 INTRODUCTIONAND OBJECTIVES

Advanced aircraft propulsion gas turbine engines for civil

and military applications must provide increased power density

usually expressed in terms of thrust or horsepower per unit airflow. Higher cycle pressure ratio and turbine inlet temperature

(TIT) offer the greatest potential for increasing engine performance and reducing engine weight and size. However, because of the

higher average TIT, the gas temperature distribution must be

closely tailored for acceptable radial temperature profile and

minimal peak gas temperature.

The combustor discharge temperature quality is influenced by

nearly all aspects of the combustor design and in particular by

the dilution zone. Due to increasing burner inlet air temperature

and fuel/air ratio, an increasingly higher fraction of the combustor through-flow air is needed for combustion and cooling with

correspondingly reduced airflow available for dilution purposes.

An improved understanding of dilution jet mixing processes

will result in effective utilization of the available dilution

air. The present program has been undertaken to acquire a data

base of dilution jet mixing characteristics to develop empirical

jet mixing correlations and validate combustor analytical design

models.

The penetration and mixing of air jets directed into a crossstream have been investigated by many researchers. Jet trajectory

and mixing models have been developed both empirically and analytically. In the majority of the studies, the models are not

directly applicable to flows in gas turbine combustion systems due

to either an inappropriate range of flow conditions or unrealistic

test geometries. In almost all cases, correlations have been

derived using single jets discharging into a uniform cross-flow in

relatively large ducts. In gas turbine combustion systems, a
number of dilution orifices in single or multiple rows normally

inject the cooler air into relatively small annular ducts with

non-uniform flow fields, resulting in jet interaction with

adjacent jets and the liner walls. The availability of experimental data to extend current jet mixing models to account for

these factors is limited, which results in only qualitative application of the models by combustion engineers in actual design

practice.

The work reported in References 1 through 4 for multiple-jet

injection into a confined cross-stream provided the basis for the

program reported here. The nominal cross-flow test conditions in

those studies were: Um = 15 m/sec; T_ = 600°K with uniform temperature and velocity profiles. Dilution jet velocities (Vj)

varied over the range of 25 m/sec to 85 m/sec with jets at an

ambient temperature Tj = 300°K. The test conditions were established based primarily on jet to mainstream momentum ratio

(J = Pj Vj2/PmUmZ)- variation from 6 to 60, with density-ratio

(Pj/Pm) variation from 1.5 to 2.5.

Jet mixing correlations were developed (References 2 and 4) in

terms of the momentum ratio and the following geometric variables:

o 2_< S/D <-6 D = Dilution orifice diameter

o 4-< Ho/D <_16 H o = Channel height at injection

plane

o 0.25_< X/H o-< 2

o 0 < Z/S < 0.5

X = Axial flow direction

Z = Lateral flow direction

= Orifice spacing along the

transverse direction
The main objective of the NASA Dilution Jet Mixing Phase I

Program was to quantify the effect of the following factors on jet

penetration and mixing:

o

o

J, Ho/D, S/D, pj/p_

Non-uniform cross-stream temperature and velocity main

profiles upstream of dilution orifices

o Cold versus hot jet injection

o Cross-stream flow area convergence (accelerating crossstream) as encountered in practical dilution-zone geometrieso

The experimental effort was divided into four series of

tests:

Series 1 test objectives were to evaluate current data in

relation to previous data and correlations at comparable conditions for jet mixing in a uniform cross-stream and to compare

mixing characteristics of a cold jet injected into a hot stream

versus a hot jet injected into a cold stream.

The effects of mainstream velocity and temperature profiles

on jet mixing processes were investigated in Series 2 test. Two

types of cross-stream temperature profiles were studied. A profile generator was used to inject a cooler stream near the jet

injector wall with an increasing temperature profile away from the

injection wall. A decreasing radial temperature profile was used

in the second set of investigations.

Dilution zone geometric details, including flow area convergence rate and shape (symmetric or asymmetric convergence),
affect jet penetration and downstream radial profiles. The effect

of mainstream acceleration on jet mixing behavior was studied in

Series 3 tests. Both symmetric and asymmetric converging test

sections were used in this test series.

Practical dilution zone designs include both flow convergence

and profiled cross-stream. A limited study was done in Series 4

tests on quantifying the effect of flow convergence as well as

cross-stream profile on jet spreading.

In addition to the four test series described above, limited

model validation and correlation were done based upon the extension

of the correlations developed by Holdeman and Walker

(Reference 2).
3.0 TEST RIG AND FACILITY DESCRIPTIONS

3.1 Test Riq

A schematic layout of the jet mixing test rig is presented in

Figure 2 and a partially assembled rig in Figure 3. The mainstream airflow is ducted from the test cell main air supply

through a 15.24-cm internal diameter pipe. A transition section

connects the inlet pipe to a rectangular cross section of constant

width (30.48 cm) and adjustable height.

A perforated plate with 25 holes of 1.43-cm diameter provides

a relatively uniform airstream upstream of the profile generator

plenum. The profile generator duct incorporates an adjustable

bottom wall to match the test section inlet height, which can vary

from 10.16 cm to 15.24 cm.

A separate air supply enables the profile generator to provide the desired radial profile of temperature and velocity

upstream of the jet-injection plane.

A third air supply allows the dilution injection orifices to

vary jet velocity and density. A number of interchangeable dilution orifice plates and test section geometries were used to study

confined jet mixing with the mainstream. To minimize the rig heat

losses, the rig walls were insulated with a 2.54-cm thick layer of

Kaolite insulation.

In addition to a traversing Pt/Ps/T rake, as shown in

Figure 2, the rig instrumentation includes a number of wall static

pressure taps and flow thermocouples.

A brief description of the profile generator, test sections,

and dilution orifice plates is provided in the following paragraphs.
3.1.1 Profile Generator

A profile generator (Figure 4) provides a desired radial profile in the mainstream. This is achieved by varying independently

the flow conditions of the approaching mainstream and the flow

injected from the profile generator. As shown in Figure 2, a

separate air supply is used to vary the temperature and velocity

of the air supplied to the profile generator slot, which is

2.54-cm high and 29.2-cm wide. The slot is fed uniformly through

an inclined perforated plate having 50 orifices of 1.47-cm

diameter; these orifices can be seen in Figure 4. The supply-air

duct dumps the air into a rectangular plenum (or settling chamber)

of 30.48 x 16.75 x 12.7-cm dimensions.

Three wall static pressure taps and one thermocouple were

used to control the plenum air pressure and temperature levels,

which, along with the main supply flow condition, control the

mainstream radial profile.

3.1.2 Test Sections

In the present study, jet mixing was characterized for four

different test sections, as pictured in Figure 5; their important

dimensional parameters are summarized in Table I. Both constantheight and variable-height test sections were investigated.

Test Section I has a constant channel height (H ° = 10.16 cm)

and slightly more than 2H o length to allow radial profile measurements at X/H o = 0.5, 0.75, 1.5, and 2.0.
TABLE I. DEFINITION OF TEST SECTIONS

Test

Section

Number

II

III

IV

V

VI

Description

Constant

Height

Symmetric

Convergence

Symmetric

Convergence

Symmetric

Convergence

Asymmetric

Flat-Wall

Injection

Asymmetric

InclinedWall

Injection

Test Section

Height

-Injection

Plane

10.16

10.16

10.16

10.16

i0.16

10.16

icm)

Exi£

Plane

10.16

5.08

7.62

5.08

5.08

5.08

Jet

Injection

Angle

(Degrees)

90.0

97.i

97.i

104.0

90.0

116.6

Test

Section

Convergence

Rate

-dh

dx

0

0.25

0.25

0.50

0.50

0.50

The same piece of hardware was used for Test Sections II and

III, which are symmetrically converging with a wall inclination

angle equal to 7.1 degrees. Consequently, the jet injection angle

is 97.1 degrees. The test section flow area convergence rate

(defined as -dh/dx) is 0.25. Test Section II exit-plane height is

5.08 cm at X = 2 Ho, and the corresponding injection to exit plane

area ratio is 2.0. Test Section III is assumed to be 10.16-cm

long with attendant exit-plane height of 7.62 cm and area ratio

equal to 1.33.
Test Section IV is symmetrically converging with a convergence rate of 0.5; the corresponding inclination angle is 14.0

degrees for both top and bottom walls. Therefore, the jet injection angle is 104 degrees. The test section injection to exit

plane area ratio is 2.0.

Test Sections V and VI are asymmetric with a convergence rate

equal to that of Test Section IV. The bottom wall of Test

Section V is horizontal and the top wall inclination is

26.6 degrees with an attendant jet injection angle of

116.6 degrees. By turning Test Section V, the top wall becomes

flat (horizontal) and the jet injection angle becomes 90 degrees.

It should be noted that all test sections have a 10.16-cm

channel height at the injection plane. Consequently, the inlet

channel heights of the test sections range between 10.16 and

15.24 cm. To match the test section height, the profile generator

section height was adjusted by means of a moveable wall.

To insure well-controlled boundary layer profile at the

injection plane, a boundary-layer trip (0.41-cm high and 0.33-cm

wide) was welded to all four walls of the test sections. The trip

is located 15.24 cm upstream of the jet injection plane.

A number of static pressure taps are installed on all four

walls of the test sections. As delineated in Figure 6 for Test

Section I, a total of 32 wall statics are used to measure static

pressure distribution. Four thermocouples (two thermocouples

extending from the top wall and two through the bottom wall) are

used for monitoring the mainstream gas temperature levels. These

thermocouples are immersed 1.27 and 3.81 cm from the bottom and

top walls, respectively.
3.1.3 Dilution Orifice Plate Geometry

Four circular orifice configurations, illustrated in

Figure 7, were used on the present investigation. These plates

are designated by 3-set numerals indicating aspect ratio, S/D, and

Ho/D. The aspect ratio is unity for the circular orifices. Two

orifice spacings (S/D = 2 and 4) were investigated. Similarly,

two orifice sizes (D = 1.27 and 2.54 cm) were employed, producing

Ho/D = 8 and 4, where H o (test section height at the injection

plane) is equal to 10.16 cm. Table II gives important dimensions

of the four dilution orifice plates used in the present study.

TABLE II. DESCRIPTION OF DILUTION ORIFICE PLATES

Orifice

Diameter, D Number of

Designation (cm) Orifices S/D Ho/D S/H °

01/02/04 2.54 6 2 4 0.50

01/04/04 2.54 3 4 4 1.00

01/02/08 1.27 12 2 8 0.25

01/04/08 1.27 6 4 8 0.50

3.2 Test Facilities

The test rig was installed in the combustion test cell,

C-100. Three air supplies were used for setting up the required

flow conditions for the mainstream, profile generator, and dilution jets. Nonvitiated air from the laboratory compressors and

heaters was used throughout the present investigation.

i0
The mainstream air temperature can be regulated from ambient

to 725°K. A special preheater is used for obtaining air temperatures above 750°K. For the majority of the test cases the mainstream nominal temperature and flow rate were 644°K and 0.25

kg/sec, respectively. For the test cases involving hot jet injection the mainstream nominal temperature and flow rate were 310°K

and 0.56 kg/sec, respectively. The mainstream temperature was

measured by thermocouples located at the test section entrance. A

standard ASMEorifice section installed in a 15-cm inside diameter

pipe was used for measuring the mainstream airflow rate.

A second, separately controlled air supply was used for the

profile generator, which can be installed in either the top or

bottom walls of the test rig. The mainstream profile was adjusted

by varying the pressure drop across the profile generator and the

attendant airflow rate. The airflow rate was measured by an ASME

orifice in a 7.62-cm inside diameter pipe.

A third air supply was used for controlling the dilution jet

flow conditions, including jet velocity and temperature. For a

majority of test cases, the dilution jet air was at ambient temperature and therefore no external heater was required. For hot

jet injection, an external heater supplied a nominal dilution air

temperature of 450°K. The dilution airflow rate was measured by

an orifice section in accordance with standard ASME airflow measurement procedures.

ii
4.0 DATAACQUISITION AND REDUCTION

4.1 Data Acquisition

The dilution jet mixing characteristics were determined by

measuring temperature and pressure distribution within the test

section at different axial stations. A traversing probe, shown in

Figure 8, was used for this purpose.

The probe consists of a 20-element thermocouple rake surrounded by 20 total-pressure sensors on one side and 20 staticpressure rakes on the other side. The nominal transverse spacing

between the thermocouple rake and the total pressure rake is 5.08 mm;

similarly, the spacing between the thermocouple and the static

pressure elements is 5.08 mm.

The center-to-center height of the probe is 9.35 cm. The

first element is therefore located 4.05 mm from the top wall of

the constant-height test section, i.e., 0.16 D for a 2.54-cm dilution jet diameter. All the elements are equally spaced in the

vertical direction, providing a nominal spacing of 4.92 mm.

The total-pressure sensor elements are made of Inconel tubes

with an outside diameter of 0.16 cm and a wall thickness of

0.023 cm. The internal conical design of the tube at the inlet

provides a ±15 degree flow insensitivity angle. The static pressure tubes, similar to the total pressure sensors, are dead-ended

with four bleeding holes of 0.03-cm diameter 90 degrees apart and

0.7 cm from the tip. The total temperature sensors are type K

thermocouple wires with insulated junctions encased in 0.10-cm

inside diameter tubes, supported by 0.21 cm inside diameter

enveloping tubes. The insulated junction tubes exposed to the air

stream are 0.76-cm long. All the sensing elements have a straight

length of 1.52 cm or more before the first bend to the probe core

12
where all tubes are inserted in a rectangular probe shield,

4.32 cm x 0.67 cm.

The probe is mounted on a traversing system (Figure 9) that

allows travel in three directions. This system allows 30.48 cm

traverse in the X-direction (mainstream flow direction) and

22.86 cm in the radial (Y) and lateral (Z) directions with an

accuracy of ±0.015 percent. The flow field mapping in the

Z direction is done over a distance equal to the hole spacing (S)

for any given orifice plate. The measurements in the Z direction

were made at the planes identified by Z/S = 0, 0.i, 0.2, 0.3, 0.4,

0.5, 0.6, 0.7, 0.8, 0.9, and 1.0, where Z/S = 0 denotes center of

the orifice. The measurements in the X-direction were made at the

planes X/HO = 0.5, 0.75, 1.0, 1.5, and 2.0. The probe was

traversed over a matrix of ii x 5 survey locations.

The temperature and pressure values from the test rig instrumentation were recorded on magnetic tapes through a central computerized data acquisition system. An on-line data display system

provided real-time information on selected raw data for monitoring

the flow conditions. The raw data from the magnetic tape were

later used for detail data reduction, analysis, and correlation.

4.2 Data Reduction

The rectangular grid network at which the measurements were

made can be described with the aid of Figures 1 and i0. The

X-axis is the axis along the length of the duct in the direction of

the bulk flow. The X=0 station is located at the jet injection

plane. The Y-axis (radial direction) is the direction along the

jet injection direction. The Y=O plane is located at the jet

orifice exit plane. The Z-axis is in the cross-stream direction.

The Z=0 plane is the vertical X, Y plane at a jet centerline. The

13
streamwise (X) and radial (Y) distances are nondimensionalized by

Ho, the channel height at the jet injection plane. The lateral

distance, Z, is nondimensionalized by S, the dilution orifice

spacing.

The measured gas temperature distributions are presented in a

nondimensionalized form as:

where,

8(X, Y, Z) =

T - T (X, Y, Z) m

Tm - Tj

T or TMAIN = m

T. or TJET =

3

Mainstream stagnation temperature

Jet stagnation temperature

T(X, Y, Z) = Stagnation temperature at the point (X, Y, Z) in

the flow field.

is a measure of the temperature change due to the jet at any

point (X, Y, Z) compared to the maximum possible temperature

change. 8 can vary from 0.0 to 1.0. 8 = 0.0 when the local temperature equals the mainstream temperature and 8 = 1.0 when the

local temperature equals the jet temperature. When the jet and

the mainstream are perfectly mixed, the local temperature reaches

ideal equilibrium temperature, TEB, given by

TEB = {m_T_ + mj Tj 1

\ {n_+ mj

The ideal equilibrium theta (SEB or THEB) is defined as

14
@ = T m - TEB

EB

T m - Tj

This parameter, 8EB , provides a measure of the quality of the jet

mixing. The arithmetic average temperature (T_,) at any X plane

and the corresponding Oav /= Tm- Ta[lare also _presented with the

\ Tm- Tj /

reduced data to provide the information on the average value of

the temperature field at that plane.

The measured _ values are presented in three-dimensional

(isometric) plots at each X-station. The measured 8 values are

also presented in the form of isopleths for each X-station for the

purpose of detailed comparison with correlations. These plots are

presented over a 2S span in the Z direction by assuming symmetry

of the _ distribution with respect to the midplane between two

orifices. This assumption was invoked only for the purpose of

improving the clarity of visual presentation of the temperature

distribution. The accuracy of this assumption depends upon the

uniformity of flow distribution across the jet orifices. Preliminary tests were performed to ensure that the jet mass flow was

uniformly distributed over the entire orifice plate configuration.

The isometric plots provide a convenient means of presenting the

jet trajectory and mixing. Furthermore, a comparison of the data

and correlations is presented in a two-dimensional (2-D) plot of

versus Y/H o along the jet centerplane at each of the X/H o

stations.

The pressure recordings from the probe rake were used to compute the velocity IV(X,Y,Z)) at the point (X,Y,Z). An interpolation scheme was used to compute the total pressure (Pt) and static

pressure (Ps) values at the point where probe thermocouples are

located. From these total and static pressures, a nondimensionalized velocity, V(X,Y,Z)/Vj, was computed. V(X,Y,Z) is obtained

from

15
V(X,Y,Z) = [2 (Pt (X,Y,Z) - PS (X,Y,Z))/p(X,Y,Z)]I/2

The jet velocity, Vj, is calculated from

Vj = 4 mj / (Pj NTrD 2 CD)

where D is the orifice diameter, N is the number of orifices, pj is

the jet density (Pj/RTj), and C D is the orifice discharge coefficient.

The orifice discharge coefficients were determined by measuring the pressure drop across the orifice plate (without crossflow) for a range of mass flow rates. The discharge coefficient,

CD, was obtained from the relation

A__PP = 1.99 Iw] ___c_c 2

P L ACDJ

where, wc is the corrected flow rate in ibm/sec and A is the geometric area of the orifices in square inches•

Note: w c Wa v_- T(°R) and $ = P(psi)

= 8 ' _ = 517 ' 14.696

The velocity vector in the vicinity of the jet injection

plane is predominantly in the radial direction. In such regions,

the velocity values obtained from the rake probe are not expected

to be accurate. For the sake of brevity, the measured velocity

distributions are not presented in this report. However, tables

of nondimensional velocity distribution, V(X,Y,Z)/Vj, will be provided for each test case in the Comprehensive Data Report (CDR) on

this program.

An important parameter relevant to the jet description is the

jet momentum ratio, J, defined as

16
where

J = PjVj2/(PmVm2 )

Pj = Jet density

Pm= Mainstream density = Pm/(RTm)

Vj or VJET = Jet velocity at the orifice Vena Contracta

V m or VMAIN = Mainstream Velocity = mm/(PmAm)

Other flow parameters of interest are:

Blowing rate, M or BLORAT = PjVj/PmV m

Temperature ratio, TRATIO = Tj/T m

Density ratio, DENRATIO = Pj/Pm

Velocity ratio = Vj/V_

The geometric parameters of importance associated with the orifice

configilcation are: S/Dj and Ho/D. , where D. is the effective jet

diameter defined by 3 3

Dj = D /C D

The quantities defined in this se_1on _'" define the geometric

and flow condit[orls of each test and are z eported along with the

reduced data.

17
5.0 EXPERIMENTAL DATA

5.1 Series 1 Tests

The purpose of this series was to investigate penetration,

radial, and lateral mixing characteristics of cold and hot dilution jets with an isothermal, confined cross-flow in a constant

channel height of 10.16 cm. The main objectives of this series

were the following:

o Comparison with the NASA/Aerojet data

o Relative mixing characteristics of cold versus hot jet

injection.

A total of 12 data sets were taken with the orifice geometrical description and nominal flow conditions listed in

Table III. Tests 1 through 8 were repeats of the cases selected

from the Aerojet study to demonstrate reproducibility of the jet

mixing data from two different rigs. Typical comparison of data

from Aerojet and the present investigation is presented in

Figure ii for the jet centerline plane at three axial stations

Orifice

Test Dia(D)

No. (cm}

1 2.54

2 2.54

3 2.54

4 2.54

5 1.27

6 1.27

7 i. 27

8 i. 27

9 2.54

10 2.54

11 1.27

12 1.27

TABLE IXI. SERIES 1 TEST CONFIGURATIONS AND FLOW CONDITIONS

Mainstream Jet

Velocity Temp. Velocity Temp.

VMAIN

S/D No/D (m/sec)

2.0 4.0 15.8

2.0 4.0 16.3

4.0 4.0 15.2

4.0 4.0 14.9

2.0 0.0 15.0

2.0 8.0 15.1

4.0 8.0 15.2

4.0 8.0 15.1

2.0 4.0 . 15.4

4.0 4.0 15.2

2.0 8.0 15.2

4.0 8.0 15.3

TMAIN VJET TJET

(oK) (a/sec) (oK)

650 26.0 308

651 52.0 300

649 25.9 307

651 52.2 304

649 51.9 300

650 103.6 299

651 52.0 302

649 104.1 299

306 109.4 511

293 103.3 408

290 102.2 445

293 97.6 457

Momentum Density

Ratio Ratio

J DENRATIO

5.7 2.11

21.6 2.13

6.1 2.12

26.7 2.17

25.3 2.13

107.8 2.29

26.3 2.19

109.0 2.30

31.0 0.62

30.6 0.66

30.2 0.67

30.5 0.65

Equilibrium

Temp

THEB

0.176

0.270

0.107

0.191

0.169

0.302

0.105

0.181

0.183

0.102

8.102

0.062

Region Measurements in

of Axial Transverse

Direction Direction

(Xl_o) z/s

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5- 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.5 - 2.0

0.0 to 1.0

0.0 to 1.0

-0.5 to +0.5

-0.5 to +0.5

0.0 to 1.0

0.0 to 1.0

-0.5 Co +0.5

-0.5 to +0.5

0.0 to 1.0

-0,5 to +0.5

-0.5 to +0.5

0.0 to 1.0

18
(X/H o = 0.5, 1.0, and 2.0) for two values of jet momentum ratios (J

= 6.1 and 26.7) with S/D = 4 and Ho/D = 4. The comparison, as

shown for Tests 3 and 4, of data from two different rigs is quite

good. Also shown in Figure ii is the predicted radial profiles,

using the NASA/Aerojet correlations.

The measured distribution of the nondimensionalized temperature, e, for a momentum ratio (J) of 5.74 and uniform mainstream

temperature, using the orifice plate 01/02/04 (S/D = 2, Ho/D = 4)

is presented in Figure 12. The top part of this figure shows the

isometric plot of the _ profiles at five axial planes of X/H o =

0.5, 0.75, 1.0, 1.5, and 2.0. The geometrical and flow parameters

of interest are provided at the top of this figure. The bottom

part of the figure shows the measured @ contours for the corresponding axial planes. The contour values were selected to cover

the range of @ values observed in the test. One of the contour

values selected is also the value equal to eEB, which is 0.1759 in

this case. The locations of jet centerline and jet direction are

indicated by the arrows at the top of each contour plot and in the

isometric plots.

The mixing performance for any given configuration can be

estimated from the deviation of e distribution about 8 A small

EB"

deviation from 8EB characterizes nearly complete mixing of the

jet and the mainstream. The eEB value for Test 1 is 0.1759, which

corresponds to Contour 3. _EB contours are deformed by the penetration of the jets. This deformation is gradually smoothed out

farther downstream. The location of the jet centerline can be

identified from the location of the largest contour value. For

Test i, at X/H = 0.5, the jet centerline is inside Contour 9,

which is at Y/H = 0.34.

The spreading of the jets in the transverse direction can be

determined from the smoothness of the contour shapes. For this

test, the presence of the individual jets can be seen at X/H = 0.5

19
and the jets quickly merge beyond X/H = 0.75. The locations of the

theta contour in the radial direction are not significantly different as X/H° increases beyond 1.0. From the 8 profiles at X/H° =

2.0 it can be seen that approximately the top half of the test section has an air temperature less than the equilibrium temperature, TEB, whereas the bottom half has hotter gases. This indicates the jets have not penetrated the test section to the bottom

wall.

The predicted theta distributions for Test 1 (J = 5.74, S/D =

2, Ho/D = 4) are presented in Figure 13. The predictions are

obtained using NASA/Aerojet correlations. The top part of this

figure shows the predicted theta contours while the bottom part

provides a comparison between measured and predicted radial profiles of theta along the jet centerplane. Details of the

NASA/Aerojet correlations are presented in Paragraph 6.1.

Although the predicted radial profiles are in good agreement

with the measured theta profiles, significant differences in the

theta contours can be observed. The predicted theta distributions

for this test case underestimate the transverse spreading of the

jets.

The measured theta distributions for Test 2 (J = 21.59, S/D =

2, Ho/D = 4) with uniform mainstream temperature (T m) are presented in Figure 14. In this case, 8EB is equal to 0.2705. The

measurements show that for J = 21.59, the jet centerline at X/H o =

0.5 is located at about Y/H = 0.6 compared to 0.34 for J = 5.7

(Figure 12). At X/H o = 0.5, the two jets can be separately identified and they merge gradually as X/H o increases. The variation in the radial penetration of the jets with increasing downstream distance is insignificant. As in Test i, there is a topcold and bottom-hot profile distribution.

2O
The predicted theta distributions for Test 2 are portrayed in

Figure 15. The agreement between the correlations and the data is

good up to X/H° = 1.0. Beyond this stations some differences in the

profiles are seen.

The measured data for Test 3, with uniform Tm, J = 6.14, S/D

= 4 and Ho/D = 4, are presented in Figure 16. In this test case,

the jets are located farther apart than the first two tests and

_EB = 0.1074. For a constant value of J, Ho/D , the effect of S/D on

the jet mixing characteristics can be inferred by comparing

Figures 12 and 16. For S/D = 4, the data clearly shows the

presence of two separate jets at all the axial stations. If the

half-width values (from the contours) are used, it can be seen

that the jets begin to merge only at X/Ho = 2.0, whereas

Figure 12 shows that the merging is essentially complete at

X/Ho = 1.0. Spreading of the contours in the radial direction

is significantly higher in Test 3 than in Tests 1 and 2. This

demonstrates that an increase in S/D results in improving the

radial mixing and decreasing the lateral spreading rate.

The predicted theta values for Test 3 are portrayed in

Figure 17. The NASA/Ae_ojet correlations slightly underpredict

the jet penetration and overpredict the _max for this configuration.

The measured results for Test 4 with uniform Tm, J = 26.7,

S/D = 4, and Ho/D = 4 are provided in Figure 18. For this test condition with _EB = 0.1915, data reveals the jets are impinging on

the opposing test section wall. The mixing in both the radial and

transverse directions is substantially enhanced farther downstream as compared to Test 2 with S/D = 2 (Figure 14).

An optimum dilution orifice spacing is quite important to

d_J1ieving the desired radial profiles. The profiles from Test 2

21
(Figure 14) and Test 4 (Figure 18) clearly illustrate this importance. The amount of dilution air in Test 2 is approximately

twice that of Test 4. At the same values of orifice diameter and

J, Test 2 provided a hub-peak (hot near the bottom wall) profile,

whereas in Test 4 a tip-peak profile was achieved.

The predicted results for Test 4 are presented in Figure 19.

Initially the correlations underpredict jet penetration, but farther down, jet impingement is predicted to occur between 1.0 and

1.5 Ho. The predicted radial profiles are in good agreement with

the data at X/H = 2.0.

In the next four tests, the effects of Ho/D parameters on the

mixing characteristics were studied. In these tests, the jet orifice diameter was reduced to 1.27 cm and the channel height was

unchanged. The resultant value of Ho/D was 8.

The measured theta distributions for Test 5 with uniform Tm,

J = 25.32, S/D = 2, and Ho/D = 8 are presented in Figure 20. This

orifice plate (01/02/08) is characterized by 12 closely spaced,

small holes (D = 1.27 cm) and a large duct height to diameter

ratio. For this plate at a momentum ratio of 25.32, the data shows

the jets have spread quickly in the transverse direction and no

individual jet shapes can be identified even at X = 0.75 HO The

gradual radial spreading of the contours demonstrates the slow

radial jet spreading rate.

The predicted results for Test 5 are included in Figure 21.

The predicted profiles are in good agreement with the data. The

theta contour lines in both predicted and measured data are essentially horizontal, indicating the completeness of the mixing in

the transverse direction. The predicted radial profiles are in

very good agreement with the data in the entire mixing region of

interest.

22
The data for Test 6 with uniform Tm, J = 107.8, S/D = 2, and

Ho/D = 8 are depicted in Figure 22° As observed in the results for

Test 5, the jet spreading in the transverse direction is nearly

complete, even at X/H° = 0.5 compared to 0.75 in the previous test

with J = 25. The data shows that even for the high momentum ratio

of 107.8, the jets do not impinge on the opposing wall. This

results in bottom-hot profiles at all axial planes.

The predicted results for Test 6 are presented in Figure 23.

The predicted profiles are in good agreement with the data up to

X/H = 1.0. Beyond this station, the predictions show different

trends compared to the data.

The measured data for Test 7 with uniform Tm, J = 26.3, S/D =

4, and Ho/D = 8 are portrayed in Figure 24. In this test, an

orifice plate with six holes of 1.27-cm diameter was used. For

this test condition, the data shows that at X/H = 0.5, the two jets

are separately identifiable. The two jets spread in the transverse direction gradually as X/HO increases. The gradual spreading

of the contours in the radial direction with increasing X/H°

describes the radial mixing characteristics. The mixing characteristics for this orifice plate (01/04/08) are similar to that of

orifice plate 01/02/04 (compare Figures 14 and 24) at the same

momentum ratio, J.

The predicted results for Test 7 are presented in Figure 25.

The predicted profiles are in good agreement with the data. With

increasing hole spacing(S), the jet penetration is increased, as

was shown previously for the 2.54-cm orifice diameter.

Figure 26 portrays the measured data for Test 8 with uniform

Tm, J = 109.0, S/D = 4, and Ho/D = 8. For this momentum ratio, the

data reveals that the jets impinge on the opposite wall at X/Ho =

0.5. The contour plots show significantly enhanced radial and

transverse directions at stations farther downstream. It may be

23
recalled that for a comparable J value no impingement was observed

with orifice plate 01/02/08, again indicating an increase in penetration with increasing S/D. The predicted results for Test 8 are

presented in Figure 27. The predictions underestimate the jet

penetration at X/Ho = 0.5 and 0.75. Jet impingement is predicted

at X/Ho = 1.0, while the data shows jet impingement at X/Ho = 0.5.

A similar trend was also observed for orifice plate 01/04/04.

The next four tests demonstrate the effect of density ratio.

In these tests, a cold mainstream and hot jets were used. Tests

were conducted with all four orifice plates and uniform mainstream

temperature distribution.

Figure 28 portrays the measured data for Test 9 with heated

jets at J = 31.0, S/D = 2, and Ho/D = 4. Comparison of these data

with the results for cold jets at a comparable momentum ratio, J,

and the same S/D and Ho/D (Figure 14) reveals very similar _ distributions.

The predicted results for Test 9 are presented in Figure 29.

It is emphasized that the NASA/Aerojet correlations do not explicitly include the effects of density ratio since it was considered

to be of second order in magnitude. However, the density ratio is

taken into account in determining the nondimensional equilibrium

temperature, eEB, which is used for predicting the theta distribution. Comparison between Figures 29 and 15 shows very nearly the

same type of profiles. These comparisons reveal the effect of

density ratio on the jet mixing characteristics is relatively

weak.

Test i0 was performed with heated jets at J = 30.64, using

orifice plate 01/04/04 (S/D = 4, Ho/D = 4). The measured theta distributions for Test i0 are depicted in Figure 30. For this case,

jet impingement is observed at X/H° = 1.0. At X/H° = 0.5 and 0.75,

the jets are separate. Beyond the point of impingement, an

24
enhanced mixing in radial as well as transverse direction is

evident.

The predicted results for Test i0 are provided in Figure 31.

The predicted profiles are in good agreement with the data. Comparison of this figure with Figure 19 shows that for a comparable

momentum ratio, jet impingement on the opposite wall is observed

with cold jets even at X/H° = 0.5. However, the _ profiles for hot

and cold jet cases are very similar.

Figure 32 shows the data for Test ii with hot jets, J =

30.19, S/D = 2, and Ho/D = 8. The jet spreading in transverse

direction is faster compared to that in the radial direction.

The predicted results for Test ii are presented in Figure 33.

The predicted _ profiles are in good agreement with the data

although the predicted 0 values are slightly higher than the measured values. Notwithstanding this difference, which is of

second-order magnitude, the correlations show the same nature of

jet mixing characteristics as the data. The data for this case

are very similar to the characteristics for cold jet injection

(Figure 20).

The measured theta distributions for Test 12 with heated

jets, J = 30.53, S/D = 4, and Ho/D = 8 are presented in Figure 34.

The data shows the presence of two individual jets at X/H = 0.5. o

The two jets mix well with each other rapidly, and at X/Ho = 1.5,

the mixing is nearly complete, as indicated by nearly horizontal

contour lines. The radial jet spreading rate is slower compared

to that in the transverse direction.

The predicted results for Test 12 are presented in Figure 35.

The predicted profiles have the same shape as the data, and the

predicted H values are slightly higher than the measured values.

The _ distributions for heated jets are quite similar to that for

25
cold jets, indicating a weak influence of density ratio on jet

mixing characteristics.

The first 12 tests presented thus far cover the Series 1

tests. In analyzing these tests, the parameter, orifice spacing (S)

to duct height (H) ratio, S/H, was considered only implicitly. For the orifice plate 01/02/08, S/H = 0.25, while S/H = 0.5

for orifice plates 01/02/04 and 01/04/08 and S/H = 1.0 for orifice

plate 01/04/04. From the results presented in this paragraph

(5.1), it is seen that the transverse or lateral mixing is

enhanced as S/H decreases. Furthermore, the jet penetration is

increased with increasing value of S/H. As reported in Reference 2, the coupling of J and S/H parameters is thus an important

criterion for describing the jet penetration and mixing characteristics.

5.1.1 Conclusions for Series 1 Tests

The Series 1 tests were conducted with constant duct height

and uniform cross-flow temperature distribution. Four different

orifice plate geometries were used to study the jet mixing characteristics. From these test data, the following conclusions are

made:

o A good agreement between the present data and previous

data and correlations (References 1 through 4) has been

obtained.

o

The jet penetration distance (Yc/Ho) increases with

increasing momentum ratio (J) and orifice diameter (D).

o For a given duct height to diameter ratio (Ho/D), the

lateral mixing, that is, the jet spreading rate in the

transverse direction, is enhanced with increasing

26
momentum ratio, J, and decreasing spacing to diameter

ratio, S/D.

o For a given S/D, the lateral mixing is increased with

increasing J and Ho/D.

o The radial mixing, that is, the jet spreading rate in the

vertical direction, is enhanced with increased jet penetration. This is highlighted in the case of jet

impingement on the opposite wall.

o The penetration of a hot jet in a cold cross-flow is

very similar to that of a cold jet in a hot cross-flow

at constant J. Although the hot jet penetration is

slightly smaller (less than 5 percent) than the cold jet

penetration at X/Ho = 0.5, the differences are minimal

farther downstream. The density ratio effects are, at

best, of second-order magnitude and can be neglected for

a first-order approximation, provided the momentum

ratio values, J, are the same.

o The NASA/Aerojet correlations are accurate to first

order and provide a useful tool for predicting the jet

thermal centerline trajectory and temperature profiles.

The temperature profiles are well described by the correlations except very close to the jet injection plane,

especially when jet impingement occurs.

5.2 Series 2 Tests

The objective of this series of tests was to investigate the

interaction of the jets with a non-uniform cross-flow temperature

distribution in a constant area duct. A non-uniform mainstream

temperature profile is generated by using the profile generator as

27
described in Section 3.0. Six tests were conducted in Series 2

with orifice geometries and nominal flow conditions as listed in

Table IV.

TABLE IV. SERIES 2 TEST CONFIGURATIONS AND FLOW CONDITIONS

Mainstream

Orifice Veloclty i Temp.

Test Dia(D} VMAIN TMAIN

NO. (Cm) IS/D Ho/D (m/sec) (o K )

I

13 2.54 12.0 4.0 16.9 524

14 2.54 4.0 4.0 15.4 672

15 1.27 2.0 8.8 15.5 616

16 1.27 4.0 8.8 18.1 567

17 2.54 2.0 4.0 16.5 538

18 1.27 4.0 8.0 18.2 545

Jet Region Measurements in

Velocity Temp. Momentum Density Equilibrium of Axial Transverse

VJET TJET Ratio Ratio Temp

(m/sec) (OK) J DENRATIO THEB

59.7 294 22.6 1.81 0.312

28.4 305 7.5 2.21 0.114

109.3 297 109.9 2.07 0.303

63.0 311 22.6 1.86 0.i00

57.9 303 22.1 1.80 0.305

72.2 317 27.7 1.76 0.107

Direction Direction

(X/Ho) z/s

0.5 - 2.0 0.0 to 1.0

0.5-2.0 -0.5to+0.5

0.5- 2.0i -0.5 to +0.5

0.5 - 2.0 0.0 to 1.0

0.5 - 2.0 0.0 to 1.0

0.5 - 2.0 -0.5 to +0.5

Tests 13 through 16 were conducted with the mainstream temperature profile cold near the jet exit plane (top) and hot at

the bottom of the duct. These test conditions are referred to as

"top cold".

Tests 17 and 18 were conducted with an inverted temperature

profile: hot at the top and cold at the bottom. These two test

conditions are identified as "top hot".

The temperature profiles used for these six tests are

depicted in Figure 36, in a nondimensionalized form, _p:

T - T (y)

max p _

_p(Y) = Tma x- Tj

where

T

max

= Maximum value of the profiled mainstream stagnation

temperature

T

p

(y) = Local value of the mainstream stagnation temperature

upstream of the jet injection plane.

28
Tj = Jet stagnation temperature.

The nondimensionalized temperature variable, @, represents

the ratio of the actual temperature change due to the dilution

jets to the maximum possible temperature change for any given flow

condition. Consequently, the value of @ will always be between 0

and i. For Series 2 tests, the maximum possible temperature

change is (Tma x - Tj). Thus, the definition of @ is modified for

the tests with profiled mainstream as

= (Tma x - T)

(Tma x - Tj)

where T is the local temperature in the mixing region. To be consistent with this definition of theta, the NASA/Aerojet correlations were also modified. Details of the modifications are

included in Paragraph 6.1.

The measured theta distributions for Test 13 with top cold

profile, J = 22.63, S/D = 2, and Ho/D = 4 are presented in

Figure 37. An extent of the radial and lateral jet spreading

rates can be obtained from the distortion and spreading of the

contours.

For Test 13, at X/H o = 0.5, two distinct jets can be associated with the dip in the contours around the jet injection locations. However, at X/H o = 1.0 and farther downstream, the contour

lines tend towards a horizontal line, indicating a tendency

towards complete lateral mixing. It is also interesting to note

that once the contour lines become nearly horizontal, the spreading in the radial direction is enhanced.

Figure 38 portrays the predicted theta distributions for

Test 13. The predicted results were obtained by superposing the

mainstream theta profile, 8p(Y), on the NASA/Aerojet correlations

29
for uniform mainstream temperature. Detailed descriptions of

these correlations are provided in Paragraph 6.1. The predicted

theta profiles are not in good agreement with the data, although

they show the same qualitative profiles. This suggests that the

superposition method is perhaps valid if a suitable scaling

parameter is employed for the profiled mainstream theta, 8p(Y).

The measured theta distributions for Test 14 with top cold

profile, J = 7.5, S/D = 4, and H/D = 4 are presented in Figure 39.

In these figures, the modulation of the @ contours around the

location of the jets is evident. Comparison of these figures

with those in Figure 37 shows a substantial reduction in both

lateral and radial mixing. This is largely due to the lower

J value and a higher S/H° ratio.

The predicted theta distributions for Test 14 are presented

in Figure 40. The predicted profiles seem to overestimate the

lateral mixing, while the jet centerplane radial profiles are in

qualitative agreement with the measured profiles. It is also

interesting to note that the major part of the differences between

the data and correlations is in the region where the profiled

mainstream temperature is cold (near the top for this test case).

The data for Test 15 are depicted in Figure 41. This test

was conducted with top cold profile, J = 109.9, S/D = 2, and Ho/D =

8. The 8 contours are nearly flat, even at X/Ho = 0.5, indicating a

high lateral mixing. The gradual movement of the contour locations toward the top wall provides an idea of the relatively slow

jet spreading rate in the radial direction. The dominance of the

mainstream profile is clearly seen in the isometric plots.

The predicted results for Test 15 are portrayed in Figure 42.

The predicted contours are horizontal lines, indicating the high

lateral mixing rate. The radial profiles between the data and

correlations are again in qualitative agreement.

3O
Figure 43 depicts the measured theta distributions for

Test 16, with top cold profile, J = 22.55, S/D = 4, and Ho/D = 8.

At X/H° = 0.5, the _ contours are modulated by the jet and these

distortions are gradually smoothed out farther downstream. The

spread of the contours in the radial direction is gradual,

indicating a slow radial mixing rate.

The predicted results for Test 16 are presented in Figure 44.

The radial profiles are in good agreement near the bottom and in

qualitative agreement near the top. This trend was also noted in

Tests 13 through 15.

The next two tests were conducted with an inverted mainstream

temperature profile, namely, hot at the top and cold at the bottom. Figure 45 portrays the measured results for Test 17 with top

hot mainstream temperature profile, J = 22.14, S/D = 2, and Ho/D =

4. The isometric plots show the dominance of the profiled mainstream. At X/H° = 0.5, the distortion of the _ contours around the

jet injection indicates the extent of jet penetration. These distortions are smoothed out at X/H° = 1.5. The radial mixing characteristics are seen from the relatively rapid changes in the contour locations in the radial direction.

Figure 46 portrays the predicted theta distributions for

Test 17. The predicted profiles are in good agreement with the

data, especially at X/Ho = 0.5. It is also interesting to note

that the differences in the profiles between data and correlations

are more pronounced in the colder part of the duct (near the bottom

in this test case).

The measured theta distributions for Test 18 with top hot

mainstream temperature profile, J = 27.69, S/D = 4, and Ho/D = 8 are

presented in Figure 47. As observed in the previous test case,

31
the lateral mixing appears to be rapid. The dominance of the profiled mainstream on the theta distribution throughout the mixing

region is seen clearly in the isometric plots.

Figure 48 presents the predicted theta distributions for

Test 18. The predicted profiles are in good agreement with the

measurements, especially at stations closer to the jet injection

plane (X/Ho = 0.5 - 1.0).

5.2.1 Conclusions for Series 2 Tests

Series 2 tests consisted of six tests with constant height

duct and profiled mainstream temperature distribution. The mainstream temperature profiles employed included both top cold and

top hot profiles. Four orifice plate configurations were used to

study the jet mixing characteristics. The following conclusions

are made from these tests:

o A new definition for nondimensional temperature, _, is

needed for analyzing the jet mixing characteristics.

o The jet spreading characteristics with profiled mainstream are very similar to those with uniform mainstream

temperature profile.

o The radial temperature profiles in the mixing region are

strongly influenced by the mainstream profiles upstream

of the jet injection plane.

o The superposition procedure used for modifying the

NASA/Aerojet correlations is reasonably good. This is

seen from the good qualitative agreement between the

data and correlations. Some of the differences in the

32
agreements may be due to the distortion of the mainstream temperature profile downstream of the jet injection plane. These differences between correlations and

data can be reduced by using an appropriate scaling

parameter on the superposition scheme employed.

5.3 Series 3 Tests

The objective of the Series 3 tests was to investigate the

penetration and mixing characteristics of cold dilution jets

injected into an isothermal cross-flow in a converging duct.

These tests can be divided into two segments based upon the geometry of the convergent ducts:

o Symmetric convergence (Test Sections II and IV)

o Asymmetric convergence (Test Sections V and VI)

For each of the test sections, two orifice plates (01/02/04

and 01/04/08) were used, and two momentum ratios were selected for

each orifice plate. A total of 16 tests were performed in

Series 3 with orifice geometrical description and nominal flow

conditions as listed in Table V. Tests 19 through 26 were conducted with symmetrical convergence, and Tests 27 through 34 were

conducted with an asymmetrically convergent test section. All the

convergent test sections used in these tests (shown in Figure 5)

have the same area ratio, Ao/Ami n = 2, where Ao is the duct area at

the jet injection plane and Ami n is the minimum area of the duct.

The results for symmetric convergence are presented in Paragraph

5.3.1 and for asymmetric convergence in Paragraph 5.3.2.

5.3.1 Symmetric Convergence Test Sections

The two symmetric convergence test sections used in these

tests were Test Sections II and IV. (See Figure 5.) Uniform

33
TABLE V. SERIES 3 TEST CONFIGURATIONS AND FLOW CONDITIONS

Orifice

Test Dia(D)

No.

19 1.27

20 1.27

21 2.54

22 2.54

23 1.27

24 1.27

25 2.54

26 1.27

27 1.27

28 1.27

29 2.54

30 2.54

31 1.27

32 1.27

33 1.27

34 2.54

Mainstream Jet

Veloclty Temp. VelOCity

VMAIN TMAIN VJET

(cm) S/D Ho/D (m/eec) (o K ) {m/sec)

4.0 8.0 15.9 656

4.0 8°0 15.5 645

2.0 4.0 15.0 654

2.0 4.0 15.8 654

4.0 8.0 17.0 646

4.0 8.0 16.9 643

2.0 4.0 15.1 643

4.0 8.0 14.9 641

4.0 8.0 16.1 646

4.0 8.0 16.0 645

2.0 4.0 15.7 645

2.0 4.0 15.6 646

4.0 8.0 16.4 649

4.0 8.0 16.5 647

2.0 4.0 16.3 650

2.0 4.0 16.2 651

58.1

106.4

28.1

54.5

53.8

i05.1

27.7

55.1

58.7

112.5

29.1

56.4

58.6

116.0

29.5

55.9

Temp. Momentum

TJET Ratio

(o x) J

330 27.1

314 102.5

308 6.7

304 26.1

312 21.1

311 05.8

322 6.7

330 26.7

320 27.2

319 106.7

314 7.1

314 27.3

320 26.6

321 107.0

301 7.1

297 26.4

Density Equilibrium

Ratio Temp

DENPJ.TIO THEB

2.02 0.106

2.19 0.188

2.13 0.197

2.18 0. 307

2. i0 0.097

2.07 0.178

2.00 0 • 183

1.96 0.299

2.05 0.107

2. O_ 0 • 189

2.0_ 0.198

2.09 0.315

2.01 O. 107

2. I_ 0 •189

2.11 0.197

2.2._ 0.314

Region

of Axial

Direction

(X/H o)

3.25 to 2.0

_.25 tO 2.0

D.50 to 2.0

0.50 to 2.0

0.25 to 1.0

0.25 to 1.0 !

0.50 to 1.0

0.50 t:o 1.0

0.25 to 1.0

0.25 to 1.0

Measurements In

Transverse

Direction

Z/S

0.0 to 1.0

0.0 to 1.0

0.0 to 1.0

0.0 to 1.0

-0.5 to +0.5

-0.5 to +0.5

0.0 to 1.0

0.0 to 1.0

0.0 to 1.0

0.0 to 1.0

0.50 to 1.0 -0.5 to +0.5

_.50 to 1.0 -0.5 to +0.5

0.25 to 1.0 -0.5 to +0.5

0.25 to 1.0 -0.5 to +0.5

0.50 to 1.0 -0.5 to +0.5

0.50 to 1.0 -0.5 to +0.5

mainstream temperature and velocity profiles were generated at the

jet injection plane. All these test sections have a duct height

(Ho) of 10.16 cm at the jet injection plane.

Test Section II is a symmetrically convergent duct with

channel height reduction from 10.16 cm (4 in.) to 5.08 cm (2 in.)

over a length of 20.32 cm (8 in.). Test Section IV has a channel

height reduction from 10.16 cm (4 in.) to 5.08 cm (2 in.) over a

length of 10.16 cm (4 in.).

Since the Series 3 tests were performed with uniform mainstream temperature profiles, the definition of theta needed for

analyzing these data is identical to those used in Series I,

namely,

T - T

_ m

Tm - Tj

34
where

T m = Mainstream stagnation temperature

T = Local stagnation temperature

Tj = Jet stagnation temperature

The measured theta distributions for Test 19 with Test Section II, J = 27.09, S/D = 4, and Ho/D = 8 are portrayed in Figure 49. For Test Section II, the jet injection angle is

97.1 degrees and measurements were made at four axial planes. For

orifice plate 01/04/08, the measurements were taken at

X/H o = 0.25, 0.5, 1.0, and 2.0. Figure 49 shows the presence of

two distinct jets at X/H ° = 0.25 and 0.5. At X/H o = 1.0, the two

jets begin to diffuse with each other and at X/H ° = 2, the contour

lines are almost horizontal, indicating nearly complete mixing in

the lateral direction.

Comparison of Figures 49 and 24 reveals the effect of convergence on the jet mixing characteristics. These two figures correspond to the same orifice configuration at a comparable momentum

ratio. For both cases, the jet centerline is located at about

50 percent of local channel height at X/H ° = 0.5 and 1.0. The jet

spreading rate in the radial direction is significantly faster in

the convergent duct than in the constant area duct. The jet

spreading rates in the transverse direction for the two cases are

nearly the same.

The predicted theta distributions for Test 19 were obtained

by modifying the NASA/Aerojet correlations for a convergent duct.

In a convergent duct, the local mainstream velocity, Vm(X),

increases with X according to the relation

V m (X) A °

V o A (X)

35
where Ao is the duct cross-sectional area at the jet injection

plane, A(X) is the local duct cross-sectional area, and Vo is the

mainstream velocity at the jet injection plane. For low Mach numbers, the density variation with X can be neglected. Thus, the

equivalent momentum ratio at any axial station can be expressed

as:

J

eq

pj V j2 Pj Vj 2 V o 2

Pm Vm 2(x) Pm Vo 2 Vm 2(x)

Thus, Jeq : J (A(X)_ 2

o /

where Jo is the momentum ratio at the jet injection plane. Predictions for convergent ducts were obtained by using the equivalent momentum ratio, Jeq' in the NASA/Aerojet correlations. These

results are presented in Figure 50 for Test 19. The predicted

radial theta profiles are in very good agreement with the data at

X/H o = 0.25 and 0.5. The agreement between data and correlations

is qualitatively good at X/H ° = 1.0 and X/H o = 2.0. The accelerating flow in the convergent duct enhances mixing in radial and

transverse directions. Although the correlations correctly predict the jet penetrations, the enhanced mixing due to convergence

is not properly taken into account.

Figure 51 illustrates the measured theta distributions for

Test 20 with Test Section II, J = 102.5, S/D = 4, and Ho/D = 8.

For this condition, the jets impinge on the opposite wall even at

X/H o = 0.25, followed by a rapid mixing in the transverse direction. The theta distributions for this case are similar in characteristics to those with constant area duct. (See Figure 26.)

The predicted results for Test 20 are presented in Figure 52.

The predicted profiles are in very good agreement with the data at

36
X/H o = 1.0 and 2.0. In regions closer to the jet injection plane,

the jet penetration is underpredicted. It is recalled that even

in Series 1 test cases, the NASA/Aerojet correlations underpredicted the jet penetrations for high momentum ratios.

The measured theta distributions for Test 21 are shown in

Figure 53. Test 21 was performed with Test Section II, J = 6.7,

S/D = 2, and Ho/D = 4. For this orifice plate, measurements were

taken at X/Ho = 0.5, 0.75, 1.0, and 2.0. At the momentum ratio of

6.76, the jets penetrate to about Y/H = 0.4 at X/H = 0.5 and o

gradually diffuse in radial and transverse directions. The radial

mixing rates in this case are slightly faster than that with

uniform duct height at the same momentum ratio. (See Figure 12.)

The predicted results for Test 21 are presented in Figure 54.

The predicted theta profiles are in good agreement with the data

at X/H° = 0.5. Beyond this station, the predicted theta values

are slightly larger, but the shapes of the @profiles are correctly predicted.

The measured theta distributions for Test 22 with Test Section II, J = 26.07, S/D = 2, and Ho/D = 4 are illustrated in Figure 55. For this momentum ratio, the jet penetration is about

60 percent of the local duct height at X/H° = 0.5, the jets gradually diffuse deeper, and at X/Ho = 2.0, the jet centerline is

located near Y/H = 1.0.

The predicted theta values for Test 22 are portrayed in Figure 56. The predicted radial profiles are in good agreement with

the data, especially in regions close to the jet injection plane.

The predicted theta values are slightly higher than the measured

values although the profile shapes are correctly predicted.

The next four test cases correspond to the measurements taken

with Test Section IV. The measured theta distribution with Test

37
Section IV, J = 21.07, S/D = 4, and Ho/D = 8 are presented in Figure 57. At X = 0.25, two separate jets are observed which rapidly

diffuse in the lateral direction. For Test Section IV, the jets

are injected at an angle of 104 degrees. The upstream component

of the jet momentum tends to enhance the mixing in both radial and

transverse directions.

Comparison of Figures 57 and 49 shows the effects of

different convergence rates. For Test Section IV, at X/H° = I,

the area ratio, Ao/A , is 2.0. For Test Section II, at X/H° = I,

the area ratio, Ao/A , is 1.33. With increasing convergence rate

(area ratio), jet penetration is also increased. Furthermore, the

lateral jet spreading rate is increased with increasing area

ratio.

The predicted results for Test 23 are presented in Figure 58.

The predicted distributions are at best in qualitative agreement

with the data. The correlations underpredict the jet penetration.

Some of these differences are due to the effects of jet injection

angle, which are neglected in the correlations. Furthermore, the

predicted theta values are slightly higher than the measured

values.

The measured theta distributions for Test 24 with Test Section IV, J = 85.84, S/D = 4, and Ho/D = 8 are presented in Figure 59. For this momentum ratio, the jets impinge on the opposite

wall, followed by an enhanced lateral mixing. Figure 60 illustrates the predicted theta profiles for Test 24. The predicted

profiles are in poor agreement with the data. The correlations

underpredict the jet penetration.

The measured theta values for Test 25 with Test Section IV, J

= 6.73, S/D = 2, and Ho/D = 4 are shown in Figure 61. For the low

momentum ratio of 6.73, the jets penetrate up to about 40 percent

of the local channel height. The mixing in the transverse direction

38
is very slow, as evidenced by the contour shapes. The predicted

results for Test 25 are portrayed in Figure 62. For this case,

the correlations overpredict the penetration and the predicted

theta values are significantly higher than the measured values.

Comparison of Figures 61 and 53 shows that the mixing characteristics for Test Section IV are very similar to that of Test

Section II.

The data for Test 26 with Test Section IV, J = 26.73, S/D =

2, and Ho/D = 4 are illustrated in Figure 63. In this case, the

jets penetrate up to about 65 percent of the channel height at

X/H o = 0.5 and gradually reach the bottom wall at X/H o = 1.0. The

individual jet contours are clearly seen until the jet centerline

reaches the opposing wall. The predicted results for Test 26 are

presented in Figure 64. The predicted profiles are in good qualitative agreement with the data. The predicted theta values are

higher in magnitude compared to the measured theta values. The

jet mixing characteristics for this case are very similar to those

with Test Section II. (See Figure 55.)

5.3.2 Asymmetric Convergence Test Sections

The following eight tests (Tests 27 through 34) were performed with asymmetric Test Sections V and VI. Test Section V is

a duct with rectangular cross-section with a flat wall on one side

and a slant wall on the opposite side, such that the channel

height reduces from 10.16 cm (4 in.) to 5.08 cm (2 in.) over a

length of 10.16 cm (4 in.). The jets are injected from the flat

wall (jet injection angle is 90 degrees).

Test Section VI has the same geometry as Test Section V, but

the jets are injected from the slant wall. The geometry of the

test sections is illustrated in Figure 5.

39
The tests with asymmetric converging ducts were performed

with orifice plates 01/02/04 and 01/04/08, with two momentum

ratios for each orifice plate as listed in Table V. Measurements

were made at X/Ho = 0.25, 0.5, and 1.0 with orifice plate 01/04/08

and at X/Ho = 0_5, 0.75, and 1.0 with orifice plate 01/02/04.

The measured theta distributions with Test Section V, J =

27.18, S/D = 4, and Ho/D = 8 are portrayed in Figure 65. At X/Ho =

0.25, the jet centerline penetration is at about Y/H = 0.5 and the

jet gradually penetrates farther with increasing X/Ho, but does

not reach the opposite wall.

Figures 57 and 65 provide a comparison between the jet mixing

characteristics for symmetric convergence and asymmetric convergence with flat wall injection. These two figures show nearly the

same theta distribution at all X/Ho locations. This suggests that

the jet mixing characteristics for flat wall injection are almost

identical to that in a symmetrically convergent duct at the same

orifice and flow conditions.

The predicted results for Test 27 are presented in Figure 66.

The predicted profiles are in very good agreement with the data

except at X/Ho = 1.0. The theta values predicted are slightly

higher than the measured values at most of the axial stations.

The measured theta values for Test 28 with Test Section V, J

= 106.7, S/D = 4, and Ho/D = 8 are presented in Figure 67. For

this momentum ratio, the jets impinge on the opposite wall at X/Ho

= 0.25. The jets mix rapidly in both radial and transverse directions. The jets merge with each other at X/Ho = 0.5. The predicted results for Test 28 are shown in Figure 68. The predicted

theta radial profiles are in good agreement with the data.

In this test case, measurements were made only up to Y/H =

0.'75 at X/Ho = 0.25. However, the contour plots for these cases

were obtained by using extrapolated values beyond that region.

The extrapolated values were obtained by using a cubic spline

4O
curve fit. This was done only for the purpose of clarity in

presenting the data.

Comparison of Figures 67 and 59 shows that the asymmetric

convergence with flat wall injection has the same theta distribution as the symmetric convergence with the same area _eduction.

The test results for Test 29 with Test Section V, J = 7.07,

S/D = 2, and Ho/D = 4 are illustrated in Figure 69. At this low

momentum ratio, the jets remain separate as far downstream as X/Ho

= 1.0. The radial and lateral mixing rates are quite slow as

evidenced by the shape and size of the contours. The predicted

results for Test 29 are presented in Figure 70. The predicted

radial profiles are in qualitative agreement with the data, and

the predicted theta values are significantly higher than the measured values. This trend has been observed for most of the

Series 3 tests. Furthermore, the predicted jet penetrations are

slightly deeper than that seen from the test data for this case.

The theta distributions for this test case are very similar to

those with symmetric convergence. (See Figures 61 and 69.)

The measured theta values for Test 30 with Test Section V, J

= 27.31, S/D = 2, and Ho/D = 4 are presented in Figure 71. At X/Ho

= 0.5, the jets penetrate up to about 65 percent of local channel

height and they gradually reach the opposite (slant) wall at

X/Ho = i. The jet spreading rate in the radial direction appears

to be faster than that in the transverse direction. The predicted

theta distributions for Test 30 are portrayed in Figure 72. For

this test condition, the predicted and the measured radial profiles are in good agreement at X/H° = 0.5 and are in only qualitative agreement farther downstream. As observed in the other test

cases in Series 3, the predicted theta values are slightly higher

than the measured values. Figures 71 and 72 show distributions

very similar to those in Figures 63 and 64. This re-emphasizes

the similarity in the jet mixing characteristics of Test Sections IV and V.

41
The following four test cases were taken with Test Section VI, where the dilution jets were injected from the slant

test section wall. The jet injection angle for these cases is

106.6 degrees. The jets are injected in the upstream direction,

and are expected to alter the mixing characteristics compared to

the 90-degree injection case associated with Test Section V. Comparison of the data for these two test sections provides information about the mixing characteristics at two different injection

angles with asymmetric convergence.

The measured theta distributions for Test 31 with Test Section VI, J = 26.59, S/D = 4, and Ho/D = 8 are given in Figure 73.

At X/H° = 0.25, the jet penetration is at about 60 percent of

local duct height and the penetration gradually increases farther

downstream. The lateral mixing is significantly higher for this

test section compared to that with Test Section V. (See Figure

65.) This is primarily due to the upstream injection.

The predicted theta distributions for Test 31 are portrayed

in Figure 74. The correlations underpredict the jet penetration

and overestimate the theta values compared to the measurements.

The correlations do not properly account for the effects of the

jet injection angle, which is primarily responsible for the poor

agreement with the data.

Comparison of Figures 74 and 66 reveals that the correlations

predict the profiles more accurately for flat wall injection than

for slant side injection. Furthermore, it is seen that the jet

penetration with slant side injection is deeper than that

with flat wall injection.

The measured data for Test 32 with Test Section VI, J =

]07.8, S/D = 4, and Ho/D = 8 are illustrated in Figure 75. For

this momentum ratio, the jets impinge on the opposite (flat) wall.

A comparison of Figure 75 with Figure 67 for flat wall injection

42
at a comparable momentum ratio shows that with the slant wall

injection, the jet spreading rate in the transverse direction is

significantly faster, while the radial jet spreading rates are

nearly the same. The predicted results for Test 32 are illustrated in Figure 76. The correlations underpredict the penetration at X/H° = 0.25 and 0.5, and the agreement between data and

correlations is poor. At X/H ° = 1.0, the agreement between the

two centerplane profiles is very good.

Figure 77 illustrates the data for Test 33, with Test Section VI, J = 7.05, S/D = 2, and Ho/D = 4. The jets penetrate to

about 40 percent of the duct height at X/H° = 0.5 and the jet centerline and gradually return to the injection wall. Comparison

of this figure with Figure 69 shows that for slant wall injection at J = 7.05, the lateral jet spreading rate is slightly

faster than that for flat wall injection. The radial jet spreading rates are not significantly different between these two cases.

The predicted results for Test 33 are portrayed in Figure 78. The

predicted jet penetrations are slightly deeper than the measured

ones and the predicted theta values are higher than the measured

values. The correlations are, however, in good qualitative agreement with the data.

The data for Test 34, with Test Section VI, J = 26.4, S/D =

2, and Ho/D = 4 are illustrated in Figure 79. At X/HO = 0.5, the

jets penetrate up to about 70 percent of the local duct height and

reach the opposite (flat) wall at X/H° = 0.75. Comparing this

test case with Test 30 (Figure 71) shows that the lateral mixing

is enhanced with slant wall injection. The mixing in the radial

direction is accelerated after the jet centerline reaches the

opposite wall. The predicted theta values for Test 34 are portrayed in Figure 80. The correlations slightly underpredict the

jet penetration and overpredict the theta values. The higher

theta values are a result of underestimating the mixing rate in

the correlations.

43
5.3.3 Conclusions for Series 3 Tests

Interactions between a row of jets with cross-flow in a convergent duct were studied. Two geometric orifice configurations

and two flow conditions for each convergent duct were considered.

Symmetric and asymmetric convergent test sections with uniform

mainstream temperature and velocity profiles were used in Series 3

tests. The following conclusions are drawn from these tests:

o Mixing is generally enhanced by flow area convergence.

The jet spreading in radial and transverse directions

occurs within a shorter distance from the jet injection

plane than in the case with a constant area duct.

o The jet penetration is slightly reduced in symmetric

convergence Test Section II compared to those in a

constant cross-sectional area duct. For Test Section IV, the jets are injected upstream at a higher

angle toward a region of higher cross-sectional area,

where the mainstream velocities are lower. Regions of

lower mainstream velocities can be associated with a

higher apparent jet momentum ratio and hence the jet

penetration in those regions is deeper.

o For asymmetric Test Section V with flat wall injection,

the jet mixing characteristics are the same as those of

the symmetric convergent Test Section IV.

o In the asymmetric Test Section VI with slant wall

injection (jet injection angle of 116.6 degrees), the

mixing in the transverse direction is significantly

enhanced while the radial mixing is very similar to that

with flat wall injection.

44
O The modified NASA/Aerojet correlations with equivalent

momentum ratio (Jeq) yield qualitatively good comparison with the data. However, the predicted theta values

are higher than the measured values. The differences

between the two results are larger with increasing jet

injection angle. Further refinements in the correlations are needed to improve the agreement between data

and correlations.

5.4 Series 4 Tests

The objective of these tests was to study the combined

effects of flow area convergence and profiled mainstream temperature. These tests were taken with Test Section V (flat wall

injection) and with orifice plate 01/04/08. Both top cold and top

hot profiles were employed with two momentum ratios for each profile. The test configuration and flow conditions employed in this

series are listed in Table VI. Measurements were taken at two

axial stations, X/H o = 0.25 and 1.0.

TABLE VI. SERIES 4 TEST CONFIGURATIONS AND FLOW CONDITIONS

Mainstream

Orifice Velocity Temp.

Test Dia(D) VMAIN TWAIN

No. (cm) S/D Ho/D (m/sec) (OK)

35 1.27 4.0 0.0 18.7 561

36 1.27 4.0 8.0 18.8 568

37 1.27 4.0 8.0 16.0 417

38 1.27 4.0 8.0 16.0 416

Jet

Velocity Temp. Momentum Density

VJET TJET Ratio Ratio

(m/seo) (OK) J DENRATIO

70.9 308 26.8 1.86

139.1 305 109.8 2.01

40.7 319 8.5 1,32

75.4 315 30.2 1.36

Equilibrium

Temp

THEB

0.i00

0.177

0.064

0.107

Region

of Axial

Direction

(X/S o)

0.25 to 1.0

0.25 to 1.0

0.25 to l.O

0.25 to 1.0

Measurements in

Transverse

Direction

Z/S

0.0 to 1.8

0.0 to 1.0

0.0 to 1.0

0.0 to 1.0

As stated in Paragraph 5.2 for the Series 2 tests, the definition of theta used to analyze these data is

Tmax - T

8 =

T

max - Tj

45
where:

Tma x = Maximum temperature of the profiled mainstream.

T = Local stagnation temperature in the mixing region.

Tj = Jet stagnation temperature.

The measured theta distributions for Test 35 with top cold

profile, J = 26.82, S/D = 4, and Ho/D = 8 are depicted in Figure 81. The jet penetration in this case is about 40 percent of

the channel height at X/H o = 0.25. The jets retain their individual shapes at both X/H ° = 0.25 and 1.0. The mainstream temperature (top cold) profile seems to inhibit the lateral and

radial mixing. This is evident by comparing Figure 81 with the

data for uniform mainstream profile (Figure 65). The predicted

theta values for Test 35 are portrayed in Figure 82. The predictions are obtained by superposing the mainstream theta profile

[0p(y)] on the NASA/Aerojet correlations with equivalent momentum

ratio, Jeq' in a manner similar to the one described in Paragraph 5.2. The predicted radial profiles along the jet centerplanes are in qualitative agreement with the data at X/H o = 0.25

and in poor agreement with the data at X/H ° = 1.0.

The data for Test 36 with top cold profile, J = 109.8,

S/D = 4, and Ho/D = 8 are illustrated in Figure 83. At

X/H = 0.25, the jet centerlines are located at about 60 percent

o

of local channel height. The mixing in the transverse direction

is much slower than in the corresponding test case with uniform

mainstream temperature profile (Figure 67). The predicted theta

distributions for Test 36 are presented in Figure 84. The comparison of predicted and measured radial profiles is poor.

The measured theta distributions with Test Section V, top hot

mainstream temperature profile, J = 8.51, S/D = 4, and Ho/D = 8

46
are depicted in Figure 85. At X/H° = 0.25, the jets retain their

individual shapes and mix rapidly in the transverse direction.

This characteristic is contrary to the trend observed with the top

cold mainstream profile. The predicted theta values for Test 37

are portrayed in Figure 86. At X/Ho = 0.25, the agreement between

data and correlations is good. At X/Ho = i, the agreement is

poor.

The measured theta values for Test 38 with top hot profile,

J = 30.24, S/D = 4, and Ho/D = 8 are presented in Figure 87. At

X/Ho = 0.25, the jets penetrate to about 50 percent of the channel

height and gradually penetrate to the opposite wall at X/Ho = 1.0.

The shape and location of the contours indicate enhanced mixing in

both radial and transverse directions in comparison with those

with top cold profiles (Figure 81). The predicted theta distributions for Test 38 are presented in Figure 88. The correlations

and data are in good agreement at X/H° = 0.25, while the agreement

is poor at X/Ho = 1.0.

5.4.1 Conclusions for Series 4 Tests

Confined jet mixing characteristics were studied with flow

area convergence and profiled mainstream temperature. Four tests

were performed with orifice plate 01/04/08, including top cold and

top hot mainstream temperature profiles.

The following conclusions are drawn from the data:

o Mixing of the jets in radial and transverse directions

is inhibited with top cold mainstream temperature profile and is not significantly affected with top hot profile when compared to tests with isothermal mainstream

conditions.

47
o The mainstream temperature profile has a dominant influence on the temperature distribution throughout the

mixing region.

o The superposition scheme used in the correlations is

inadequate for predicting the temperature distribution

with flow area convergence and profiled mainstream.

48
6.0 JET MIXING CORRELATIONS DEVELOPMENT

A number of empirical and semiempirical methods have been

developed by various researchers for predicting jet interaction

with a cross-flow. These models were mostly concerned with jet

blockage, entrainment, and mixing in the wake region (References 5, 6, and 7). Empirical models have been proposed for jet

trajectory, jet spread, and mixing rate. The main differences

between the various models were in the postulated mechanisms for

jet entrainment and trajectory.

Most of the popular approximate predictive techniques (References 8 through 12) employ integral methods with simplifying

assumptions introduced for mathematical simplicity.

One of the unknowns in integral mixing field prediction

methods is usually the shape of the jet cross section. The complex jet cross-section geometries are often approximated by

rectangles, circles, or ellipses for satisfying the conservation

of mass, momentum, and energy. The second unknown is a velocity

profile parameter, which is usually modeled by an appropriate

similarity assumption. These models are invalid for curved jets.

The jet deflection is treated in two ways: The first

approach treats the jet as a solid body and uses discharge coefficients for the cylinders or ellipses, together with a pressure

dif[erential across the jet in the mainstream direction to compute

the jet deflection. The second approach deals with mass and

momentum entrained from the mainstream into the jet through

empirical models and this approach is generally considered to be

more accurate. The correlations used in this study are the

NASA/Aerojet correlations, which are described in the following

paragraph.

49
6.1 NASA/Aerojet Correlations

The correlations developed by Holdeman and Walker (Reference 2) are based upon experimental data involving a row of jets

injected into a confined cross-flow. The jet centerline trajectory is given as:

Correlations for Predicting the Centerplane Temperature Profiles

Thermal Trajectory (Centerline):

(5.1)

where 10 <X)2 <_ _)]

b = .091

The results for temperature field are presented in nondimensional form by using

= (T m - T) / (T m - Tj)

where T m is the undisturbed mainstream stagnation temperature, T

is the local stagnation temperature in the mixing region, and Tj

is the stagnation temperature of the jet. The variable 8 represents the ratio of actual temperature change to the maximum possible temperature change due to the dilution jets. The centerline

temperature is correlated by the following expression:

Centerline Temperature Difference Ratio:

co [40 1 (5.2)

5O
where

and

8EB = mm Tm + mj Tj

(_m + _j)

The temperature difference ratio, 8, at any point in the

flow field is determined from:

+ +

m

= _min + (Pc @min ) exp (5.3)

where 8 ±

mln

+

and WI/2 are defined as follows:

Minimum Centerplane Temperature Difference Ratios:

where

c + = 0.038 jl "62

+ • +

8min,o = 1- e -c

8c,o

-3.67 i.I

(5.4)

m

emin_° = 1- e -cec,o

where

Centerplane Half-Widths:

0.9

(5.5)

W_/2,o

D.

3

= 0.162

0.5 0.5

(5.6)

51
.ii2oo020j0.l_%1027(_)0._ (_)

3

0.12

(5.7)

+

The half-widths WI/2 are the distance between the jet centerline

+

and the location where 0 = (0 c + 0min)/2.

Correlations for Predicting the Off-Centerplane Variation of the

Temperature Profile Scaling Parameters

Off-Centerplane Penetration

where

= I- e -g

Ycro

g = 0.227 j0.67

(5.8)

Off-Centerplane Maximum Temperature Difference Ratio

0c'Z = l- e

0c to

(5.9)

where

d = 0.452 j0.53

Off-Centerplane Minimum Temperature Difference Ratios and HalfWidths

+ +

0min_Z 0min_q

@c,Z _,o

(5.10)

52
These correlations provide a useful and reasonably accurate

prediction of the temperature profiles along the jet centerplanes.

However, the predicted off centerplane temperature profiles are

not very accurate and need refinement. Furthermore, the correlations are inaccurate for high momentum ratios when the jets penetrate to the opposite wall.

The NASA/Aerojet correlations described in this Paragraph (6.1) were derived for a uniform flow area and uniform mainstream conditions. When a non-uniform mainstream temperature profile exists, the NASA/Aerojet correlations for theta, eNA, can be

assumed to represent the changes in the local mainstream temperature distribution by dilution jets. In other words,

aNA = (Tm(y) - T) / (T m(y) - Tj) (5.11)

Here, aNA represents the results from equation (5.3).

For flows with non-uniform profiled mainstream, the ratio of

actual temperature change to the maximum possible temperature

change due to the jets is obtained from the following definition

of nondimensionalized temperature difference ratio:

= (Tma x - T) / (Tma x - Tj) (5.12)

where:

T

max Maximum stagnation temperature of the undisturbed

mainstream profile

T = Local stagnation temperature

T.

3

= Jet stagnation temperature.

53
Using equation (5.12), the profiled mainstream theta, 8m (Y)'

can be defined as

8m(y) = [Tmax - Tm(Y)] / (Tma x - Tj) (5.13)

From equations (5.11), (5.12), and (5.13) it is seen that

@ = @m (y) + [i - 8m(y)] 8NA (5.14)

Equation (5.14) is used to generate the predicted theta

values for test cases in Series 2 and 4. It is important to note

that the variation of the nondimensionalized temperature, 8, is

conveniently scaled between 0.0 and 1.0. The nondimensional temperature distribution, @NA' is obtained from the NASA/Aerojet

correlations (Equation 5.3).

For test cases with flow area convergence, the following

modifications are used in obtaining predictions. For converging

ducts at low Mach numbers, the average mainstream velocity

increases by the relation

V m(x) = V O IAol A---_X-f (5.15)

where :

v m (x) = Average mainstream velocity in the duct at any

given axial Station X

V o

A(X)

= Average mainstream velocity at the jet injection

plane (X = 0)

= Cross-sectional area of the duct at the axial

Station X

54

A

o

= Cross-sectional area of the duct at the jet injection plane (X = 0)
Thus,

Pm(X)Vm (x) = PoVo \A(X)/

Due to the acceleration induced by the flow area convergence,

the equivalent jet-to-mainstream momentum ratio is given by

Pj V 2 pj V 2

Jeq - Pm(X ) Vm2(x) Po Vo2 \ Ao /

= {A__.c_'_2

Thus, Jeq Jo \ Ao / (5.16)

Where, Jo is the momentum ratio at the jet injection plane.

The correlations for convergent ducts are obtained by substituting the equivalent momentum ratio, Jeq' wherever J is used

in the NASA/Aerojet correlations. This approach was found to

yield improved results compared to the results obtained from the

original NASA/Aerojet correlations. However, the correlations do

not account for the effects of jet injection angle, which have

been observed to have significant effect on the jet spreading

rates. Further work on the correlations is required to properly

account for these effects.

For test cases with flow area convergence and profiled mainstream, the correlations were obtained by combining the procedures

described for convergent ducts and profiled mainstream. The predictions obtained from these correlations are inadequate for

correctly describing the jet mixing characteristics in Series 4

tests. This is partly due to the fact that the distortion of the

mainstream temperature profile (without the jets) by the flow area

convergence is ignored in the correlations.

55
The NASA/Aerojet correlations, along with the modifications

suggested in this section, provide an excellent analytical design

tool for predicting the jet mixing characteristics in the dilution

zone of a combustor. These correlations were formed to yield

excellent qualitative agreement (and good quantitative agreement

in some of the test cases) with the measurements made in this program. Additional work is needed to improve the predictions

obtained from the correlations.

56
7.0 CONCLUSIONSAND RECO_LM/_NDATIONS

The tests made in Phase I of the NASA Dilution Jet Mixing

Program were directed toward better understanding of the mixing

processes of a row of jets injected into a ducted cross-flow. The

following conclusions are drawn from these tests:

o The jet penetration distance increases with increasing

the momentum ratio, J, and jet orifice diameter, D.

o The jet spreading rate in the transverse direction

increases with increasing the momentum ratio, J, and

duct height to hole diameter ratio, Ho/D , and decreasing

the hole spacing to diameter ratio, S/D.

o The jet spreading in the radial direction is enhanced

with increased jet penetration.

o

The jet-to-mainstream density ratio, pi/pm, has only a

second-order effect on the mixing characteristics for a

given momentum ratio.

o The temperature distribution in the jet mixing region is

strongly influenced by the mainstream temperature profile. The jet spreading rates with profiled mainstream

are similar to those with uniform mainstream. This suggests that a superposition principle could be applied to

predict temperature profiles with profiled mainstream.

o Jet mixing is generally enhanced by flow area convergence. The jet penetration is increased with increasing

upstream injection angle.

57
o The jet mixing characteristics with asymmetric convergence and flat wall injection are similar to those in a

symmetric convergent test section of the same area

ratio.

o The asymmetric test section with slant wall injection

has a significantly faster jet spreading rate in the

transverse direction.

o The radial and lateral jet spreading rates with "top

cold" mainstream profile and flow area convergence are

significantly slower compared to those with uniform

mainstream profile and flow area convergence. The jet

spreading rates are not appreciably altered with a "top

hot" mainstream temperature profile.

o The NASA/Aerojet correlations adequately predict the

theta profiles for constant area duct and uniform mainstream profile. For the case of constant area duct with

profiled mainstream, the superposition of mainstream

theta profiles on the correlations yield good qualitative results. An improved scaling parameter is needed

to obtain a good quantitative agreement with data.

o The modified NASA/Aerojet correlations with equivalent

momentum ratio, Jeq' provide improved predictions of

nondimensionalized temperature profiles. However, this

model does not properly account for the effects of jet

injection angles.

o For situations involving flow area convergence and profiled mainstream, the superposition of mainstream temperature profile on the NASA/Aerojet correlations is

58
inadequate for predicting the temperature profiles in

the mixing region. This is mainly due to the decay of

the mainstream temperature profile due to flow area convergence. Further work on the correlations is needed to

improve the predictions.

The correlations used in this program provide a very useful

and simple analytical tool for designing the dilution zone of a

combustor. However, additional work is needed to further refine

the correlations for convergent ducts and non-uniform mainstream

conditions.

59
J

f

J

f

f

f

J

t"

f

f

J

J

/ L

Z x__Vj = JET VELOCITY

COORDINATE ORIGIN IS LOCATED AT CENTER OF ORIFICE

Urn, Pro,Tm =

Vj, pj, Tj =

H0 =

H =

S =

D =

DJ =

ZTS =

Figure I.

MAINSTREAM VELOCITY, DENSITY, AND TEMPERATURE

INITIAL JET VELOCITY, DENSITY, AND TEMPERATURE

TEST-SECTION HEIGHT AT INJECTION PLANE

TEST-SECTION HEIGHT AT ANY X-Y PLANE

ORIFICE SPACING ALONG Z (TRANSVERSE) DIRECTION

ORIFICE DIAMETER

_"C D D

TEST-SECTION TRANSVERSE DIMENSION = 305mm

Multiple Jet Study Coordinate System and

Important Nomenclature.

6O
PROFILE

GENERATOR

AIR SUPPLY AI R:i-O

ORIFICE

PLATE

MEASUREMENT PLANES

BOTTO M TEMPERATU RE I

WALL PROFILE I

PROBE

TRAVERSING

MECHANISM

Figure 2. Jet Mixing Rig Schematic.

61
Figure 3. Partially Assembled Dilution Jet Mixing Test Rig.

62

MP-81927
Figure 4. Profile Generator.

63
Ao/Amin = 1

--_f Ib-- t:

Ho Hol

t 0 2.0

TESTSECTIONI

--Ao/Amin = 2.

1.25 Ho| Ho ' H2 = Ho]2I J_-=---o.5

1.o

I -1.0 0 1.0 2.0

] X/Ho

TESTSECTIONII ANDIll

TESTSECTIONIV

Ao/Amin = 2-]

1,5 Ho HOH1 = Ho/2 i}0.5"'-_

_ -1,0

-1.0 0 1.0

X/Ho

Figure 5.

64

MP-82023

TESTSECTIONV

v FLAT WALL INJECTION

-----_O_,- Y/H1

_, x'- , _ " %.O"°

-, \ --,ko_ol_ _,.o

- \ _o _' .,_-'_

_ 0

-1.0 XJHo 1.0

Jet Mixing Test Sections.

TESTSECTIONVI

INCLINED WALL INJECTIOH 7

/

/ o!2/

/ /

-1.0 0 1.0

H o = I0.16 cm.
REFERENCE

_- PLANE TO

ALL TEST SECTIONS

SIDEWALL

NUMBERS

57

UPLES

55

52

51

/

49 /

/

/ TOP WALL

/ STATIC

NUMBERS

BOTTOM WALL

STATIC NUMBER',

FLOW

39

SIOEWALL STATI C

NUMBERS

Figure 6. Test Section Wall Statics and Thermocouples.

65
._ PLATE 01104104

ii!!ii! i  ̧ i

!_ PLATE 01/02/04

[] PLATE 01/04/08

PLATE 01/02/08

MP-82024

66

Figure 7. Dilution Orifice Plate Configurations.
iiiiii_i

iii_!iii!ii_ii!iiiii

iiii!iii!iii!ii  ̧

Figure 8. Total Pressure, Thermocouple, and Static

Pressure Rake.

i 67
Figure 9. X-Y-Z Actuator with the Rake Mounted.

68

_-81922
Figure i0. Jet Mixing Rig as Viewed from Rig Discharge End.

28

69
X

Ho - 0.5

80.00 oi2o o_4o 060

0,00 0.20 0.40

THETR

(THAIN-T]/ITMRIN-TJ)

J = 6.1

1.0 2.0

8-

o

__@-

z

O-

_0.00 0-_0 0-40 0.60 _0.00 O.ZO 0,40 0.60

• I I I _. I J I

o o

0

@

° :

_, • ,,z

8

® _] °!

/° r" _ i I

0,60 _0.00 0._0 0_40 01.60 0.00 0a.20 01-40 O.BO

THETA THETA

(TMAIN-T)/[TMAIN-TJ] [TMRIN-T]/ITMAIN-TJ]

J = 26.7

[] PRESENT INVESTIGATION

0 NASA/AEROJET DATA

-- NASA/AEROJET CORRELATIO N

_0.00 0.20 0.40

• I I

o

o

a-_

-r-_.

o o

t,L._ 121O

oq

_- _

_- o o

o o

0.00 0].20 01.40

THETR

( TMA IN-T )/[ TP'IAI N-TJ ]

0.60 0.60 _0.00 0.20 0.40 0.60

o

_0-00 O.ZO 0.40

• I I

o

_8_@__ _ °mmm+_m_ m,,.,m_ _ o

o

0.00 01.20 01.40

THETFI

[TNAIN-T ]/[ TNAIN-TJ]

b

ED

130

'no

o®

o®

o

m

0.60 01.60 0.00 0].20 0].40 01.00

THETA

6TNAIN-T]/(TMAIN-TJ)

Figure ii. Typical Comparison Between Data From NASA/Aerojet

and Present Investigation for S/D = 4 and Ho/D = 4.

7O
S = 0,0508 METERS

_-_-_ _-_---_

XlNO 0.500 X/DJ X/DJ Z.44 3.67

MEASURED THETA PROFILES FOR TEST NO. 1, TEST SECTION I, TMAIN=CONST, , d = 5.74

$/0J = 2.443 HO/OJ = 4,887 VMRIN = 15,8 MIOEC YJET = 26.0 M/$EC TIISTN = 64-9.8 N TJET = 308.1 N THEB= 0,t709 8LORRT= 3,243 OENRRT[O= _,t_3 TRRTIO=O,4'74

, S,"D = Z,OO , HID = 4.00

CONTOUR t 2 3

VALUE 0.0500 0,1000 0._759

Tr4_SV_ ol_r I/8 _ -o. _ J I.o

4 5 6 7

0.2000 0.2500 0.3000 0.3500

i

8 £ [0 It

0.4000 0,5000 0,6000 0,7000

i i i I

MEASUREO THETA CONTOURS FOR TEST NO,l, TMAIN=CONST, J=5.74, 8/0=2.0. HtD=4,0

Figure 12

71
CONTOUR I 2 3 4 5 8 7 8 9 lO II

VRLUE 0.0500 0,i000 0.1759 O.ZO00 0.2500 0.3000 0.3500 0.4000 0.5000 0.6000 0.7000

i PREDICTED THETR CONTOURS FOR TEST NO. 1. TNRIN=CONST. J=5.74, 810=2.0 HID=4.0

$/0J = _.44

X/H = 0.80 X/Dd 2.44

o.w o_ o.u

%

J

[TNR IN-T 1/( TMFIIN-TJ )

HO/OJ = 4.89

XIH = 0.75 XIDJ --.3.B7

® ,;m B,_ o,_

g

D,® o_ o._ o.® o_ ,.m

(TMQIN-T)/(TMBIN-TJ)

VRQTIO = 1.65 TRRTIO : 0.4"/4 DENRRTIO=2.1t3 TtlQIN = 649.B K

X/H = !.00 X/DJ _.B£

i)m,

(TNRIN-T )/(TMQIN-TJ)

TJET = 308.1 K

XlH = 1.50 XlOJ =7.33

o.= o.w o,®

i)

#.

(TMRIN-T l/( TMQ IN-TJ )

THEB = 0.176

X/ff : _.OO X/DJ _.??

m a-., piw pi®

I"

D.= o., o_ o.w I.®

(TMQIN-T)/ITNRIN-TJ)

CONPRRt$ON BETWEEN ORTR RND CORRELRTIONS FOR TEST NO. 1. TEST SECTION I. TMRIN = CONST. J = 5.74 . S/O =2.00 , H/D =4.DO

Figure 13

72
S =0.0508 METERS S/DJ = 2.882 HO/DJ = 5.t64 VMR[N = t5.3 t'/SEC VJET = 52.0 M/SEC TMRIN = 851.2 K TJET = 308.0 K THEB = 0.2705 BLORAT= 6.281 DENRQT[O= 2.]32 TRAT[O=O.4q3

HoOj ...... ,o o 758 .. ...... soo _ x,DJ-- _.3_

MEQSUREB THETA PROFILES FOR TEST NO. 2, TEST SECTION [, TMRIN=CONST. , J =21.$8 , S/O = 2.00 , R/O = 4.00

, i , i oo

-0.5 NSV . • ,.S

CONTOUR 1 2 3 4 5 6 ? 8 9

VRLUE 0.0800 0-1200 0.1800 0,2400 0,2705 0.3800 0-4280 0.4800 0.5400

TRAN8 ERSE OIS Z 8 -8"S T_NS. ERSE DIST, Z/S I'S 1"8 ,o _S,S T. / "S

MERSURED THETR CONTOURS FOR TEST NO. 2, TMRZN=CONST, J=21.59, 8/[3=2.0, H/D=4.0

Figuze 14

73
CONTOUR t 2 3 4 5 6 "7 8 9

VRLUE 0-0600 0.1200 0.1800 0.2400 0.2705 0.3600 0.4200 0.4800 0,5400

-o.s . . _.o 4.s . [Ts i o 4.s , , _.s _.o - ' TRANSVERSEOZST. Z,$ , 1.o TRP_SVERSEOlST LS I 5

PREDICTED THETA CONTOURS FOR TEST NO.2, TMRINzCONST, J-21.5S, 5/0=2.0, H,'0=4,0

$/DJ = 2.58 HO/OJ = 5.16 VRRTIO = 3.18 TRBTIO = 0.473 DENRAT[O=2,132 TMRIN = 651 .Z K TJET = 308.0 K THE8 = O.ZT[

X/H = O.gO X/OJ _.5S X/H = 0.75 S/DJ -_.B7

_ : i-

(TNQIN-T)/(TNAIN-TJ)

X/H = L .00 X/OJ 4.t6 X/t( = 1 .go x/Do =?.TS

[ TMR[N--T ;/[ TMftIN-TJ ) _TMRIN-T )/_ TNA IN-TJ _ [ TtIRINLT )/c TMA IN-TJ

X/U = Z.O0 X/OJ =10.33

( TMf_IN-T ]/( TN£ [N_TJ ;

Figure 15

COMPARISON SETNEEN OAT_ AND CORRELATIONS FOR TEST NO. 2, TEST SECTION I .UNIFORM TMRIN. J = 21.5£ , S/O =2.00 , M/O =4.00

74
$ =0.I016 METERS 810J = 4,682 HOIOJ = 4,882 VMA[N = 15.2 M/SEC YJET = 2B.£ M/8EC TRAIN = 649,3 K TJET = 808.9 _ THEB = 0.i074 BLOR£T= 3,356 OENRAT[O= 2.122 TR_TIO=0.4?3

d_>---___ _ _,_ .,, ,p

. XIHO = 0.500

X/DJ = 2.34

NERSURED THETR PROFILES FOR TEST NO. 3. TEST SECTION I. TMRIN=CONST. . d = 6.14 , S/B = 4.00 . H/D = 4.00

- .5 TRItN,_VER_E 1318T,ZI8 I" I'°

CONTOUR t 2 3 4 5 6 q 8 9

VALUE 0.0250 0.0750 0.1074 0.1V50 0.2250 0.2750 0.3250 0.3?50 0-4250

_ t. TRR_WRSEOIST I/S mANSVERSE 01_. Z/S t.

MEASURED THETR CONTOUR5 FOR TEST NO. 3. TMRIN=CONST, J=S.14. S/B=4.0. H/D=4.0

Figure 16

75
CONTOUR 1 2 3 4 5 6 7 8 0

VALUE 0,0250 0.0"750 0.1074 0.1750 0-2250 0.2750 0.3250 0,3?50 0.4250

-o.s IRaN_S£ O_ST. Z/S _- hO m_Ve_SE OIST, Z/S _.S T_SVgRSE O_ST, ZJS .s hO

PREDICTED THETR CONTOURS FOR TEST NO.3. TNRIN=CONST, J=6.i4. 5/0=4.0, H/D=4.0

_ _ ,v_ ; _°°

/

$/DJ = 4.68

X/H = O-SO X/DJ _.34

-2s-

[TMRIN-T }I{ TtIB IN-TJ ]

HO/OJ = 4.68 VR_T[O 1-70

X/H = 0.75 X/DJ -_.St

[ TMRIN-T ]/[ TtIRIN-TJ )

TRIqTTD = 0.4"/3 0ENRRTIO=2.122

X/H = 1.00 X/DJ _.68

f-

(TMB[N-T]IITMAIN-TJJ

TCIRIN = 64$.3 K TJET = 306.9 K

X/H = t.so x/aJ =7._

o;

,/

,® o.= =_ =.= °= ,.®

(TMRIN-T]I(TMAIN-TJ)

THEB = c.107

X/H = 2.00 X/OJ _-36

a

°= o.= o._ o_ o.® ==

[TMRIN-T)/(TM£IN-TJ)

Figure 17

COMPARISON BETWEEN ORT£ RND CORRELRTIONS FOR TEST NO. 3, TEST SECTION I ,UNZFORM THRIN, d = 5.14 , S/D =4.00 , H/D =4.00 76
$ :0.1010 METERS S/DJ = 4.869 HO/DJ : 4.889 VMAIN : 14.9 M/$EC VJET = 02.2 _I/$EC TMAIN : 651.2 K TJET : 304.0 K THEB = 0.1913 BLDRIqT: 7.148 DENRRTIO= 2.174 TRIqTIO=0.4B7

4>-- _--- c>-_ 4>-

= 0.750 = 1.000 X/HO : 1 ,SOD X/HO = 2.000

3.65 _ = 4.8'7 X/DJ = 7.30 X/DJ = 9.74

MEASURED THETA PROFILE5 FOR TEST NO. 4, TEST SECTION I, TMAIN=CONST. , J =26.68 , S/D = 4.00 , HID = 4.00

CONTOUR 1 2 O 4 5 6 7 8

VRLUE 0.0500 0.1000 0,1500 0.1915 0.2500 0.3000 0.3500 0.3750

-O.B TRQNSVCRSEOIST,Z/£ I.s :.0 - " TRANSVERBEDI_T.Zz$ " I"o " TRI_N,SJERSE BIST Z S iO TRANSVERSEDIST Z/S

MEASURED THETN CONTOURS FOR TEST NO. 4, TMRIN=CONST, J=26.?, S/D=4.0, H/D=4.0

Figure 18

77
CONTOUR I 2 3 4 5 6 7 8

VALUE O,OSO0 0.1000 0.1500 0.1915 0.2500 0-3000 0.3500 0.3750

1._ t .o

reR_eesE DEST Z S

PREDICTED THETA CONTOURS FOR TEST NO.4. TMAIN=CONST. J=26.7. 8/0=4.0. H/D=4.0

Tr,_SE DIST. Z/S

$/Od = 4 .B'/

XIH = 0.50 XIDJ =_,43

HOIDJ = 4.87 VRAT IO = 3,50

X/H : 0.% X/OJ --3,B5

TP.qTIO = 0.46? DENRRTIO=_.I?4

X/H = 1.00 X/DJ =4.B?

TMAIN = 651.2 K TJET = 304.0 K

X/H = t.50 X/OJ =7.30

®

THEB = 0.192

X/H = 2.00 X/I_I _ .'74

q= o_ =.=

[TMAIN-T)/(TMRIN-TJ) {TNRIN-T)/{TMRIN-TJ) {TMAIN-T)/(TMRIN-TJ) (TNRIN-T]/_TNRIN-TJ) (TMRIN-T)/(TMRIN-TJ]

Figure 19

COMPRRISON BETWEEN DATR RNO CORRELRTIONS FOR TEST NO. 4, TEST SECTION I ,UNIFORM TMRIN, J : 26.6B . S/D :4.00 , H/O :4,00 78
5=0-0254 METERS 510J =2.582HOIOJ =10.328 VHAIN =15,0MI$ECVJET=51,9MIBECTHAIN -640.'/ K TJET=308.3 K THEB =0.108'7BLORNT= 8.890DENRATIO_ 2.128TRATIO=O,4'75

(_-;_r-'_ (_>-_--_° " ,.

<2_>

= i0.33

!_. X/HO = 1.500

MERSURED THETR PROFILES FOR TEST NO. 5, TEST SECTION I, TMRIN=CONST, , J =25.32 , S/D = 2.00 , H/D = 8,00

CONTOUR

VRLUE

_ _, _ _

.s m_B_R_ DIST, Z/S I. .o -. IR_V_,SE _[ST. _/S t.t.o

1 2 3 4 5

0.0500 0.|000 0.I68'7 0.2000 0,2500

4 5 TNN_ERSE DIST Z/5

6 7 8

0.3000 0.3500 0,4000

s Is o

MERSURED THETR CONTOURS FOR TEST NO, _, TMFIIN=CONST, J=25,32, S/I]:2,0, H/D=8.0

Figure 20

79
CONTOUR I 2 3 4 5 6 '7 8

VALUE 0,0500 O-tO00 0.168'7 0-2000 0,2500 0,3000 0.3500 0,4000

_.s I.s -o,_

TR_VI_SE o[sT, z/s lrmNsv[R_ OIST. Z/S mmNsv_6( O[ST z/s

PREOICTEO THETR CONTOURS FOR TEST NO.5, THFIIN=CONST, J=25.3, $/0=2.0, H/D=8.0

,4- J

%.

3/BJ = 2.68 HO/DJ = 10.33 VRATIO = 3.45 TRRTIO = 0.4'73 OENRRTIO:2.128 TMRIN = 648,'7 K TJET = 3O8,3 K

X/H = 0.75 X/OJ =7,76

i>8"

XlH = l,O0 X/DJ =[0.33

(THAIN-T)/(TMQIN-TJ] _TMQIN-T)/(TMAIN-TJ) (THR[N-T)/[ TMRIN-TJ)

THE9 = 0.169

X/H = 2.00 X/OJ_O.68

i

[TMAIN-T]/(TMR[N-TJI (TMRIN-TI/ITMRIN-TJ]

Figure 21

COMPRRISON BETNEEN DaTa QNO CORRELQTIONS FOR TEST NO. 5. TEST SECTION I .UNIFORH TMRIN. J : 25.32 , S/O :2.00 , H/O :8.00 80
$ =0.0254 METERS S/OJ = 2.571 HO/DJ = 10.285 VMAIN = 15.1 M/$EC VJET = 103.6 M/SEC TMAIN = 649.7 K TJET = Z99,2 K THEB = 0.3018 BLO_AT= 14,554 OENRATIO= 2.287 TRATIO=O.460

I_S_ 0500 5.14 xX/OJ ....= °.750 7.71 .... = lO,Z955

fm

=

= 20.5?

MEASURED THETA PROFILES FOR TEST NO. 6, TEST SECTION I, TMAIN=CONST. , J = 107.78 , S/D = 2.00 , HID = 8,00

CONTOUR 1 2 3 4 5 6 ? 8 9 10 11

VRLUE 0.0500 0.1000 0.1500 0.2000 0.2500 0.3018 0.3500 0.4000 0.4500 0.5000 0.5500

-o.s TmNSV_ OIST,Z/S .s " _ I_IN_[_E OIST Z/S I S * 0 _ E ll_N_S[ OIST VS

MEASURED THETA CONTOURS FOR TEST NO. S, TMAIN=CONOT, J=lOT.8, OLD=2.0, H/D=8.0

Figure 22

81
CONTOUR

VnLUE

Tm_R_ 01St, I/S

I Z 3 4 5 8 7 8 9 I0

0.0500 0.1000 0.1500 0.2000 0.2500 0.3018 0-3500 0.4000 0.4500 0.5000

i i I i i i

i.s 4._ i.t.a

_NNE DIST* _8 NN_SK 0{ST. Z/S _ER_ olsr, z/s

PREOICTED THETA CONTOUR8 FOR TEST NO.6, TMAIN=CONAT, d=lO?.8, 8/O=Z.O, HID=8.O

II

0.5800

*.o

i. _.6

81DJ = 2.57

XIH = 0.60 X/OJ_,14

m

HO/OJ = 10.29 VRRTIO = 6.86

XIH : 0.75 XlOJ :7.71

a

(TMRTN-T]I[TMAIN-TJI [THAIN-T]/(TMAIN-TJ]

TRATTO = 0,460 OENRRTIO=Z.Z87

X/H = 1.00 XtOJ =10.29

i-I

[TMRIN-T)/[TMQIN-TJ)

TMRIN = 649.7 R TJET = 299,2 K

X/H : 1.50 X/OJ =15.43

i

i

B

o.® ._ o. o= o= ,=

(THRIN-T)I(TM91N-TJ)

THEB = 0.302

X/H = 2.(X] XlOJ _0.57

_" 1-"'"

e

(TMRIN-T]/(THRIN-TJI

COMPARISON BETWEEN O_TR RND CORRELATIONS FOR TEST NO. G. TEST 8ECTION I ,UNIFORM TMRIN, d = 107.78 , 81D =2.00 , M/O =B.O0

Figure 23

02
8 =0-0508 METERS 5/0J = 5.I43 HO/OJ = [0.285 VMfqIN = 15.2 M/SEC VJEf = 52.8 WSEC TMR_N = 65[.4 5 TJET = 302.1 K THE8 = 0.1048 BLORST= ?.12"7 OENR£TIO: 2-192 TR_qTIO=0.464

--_ 4>---_,-.... 4>---_:....

4>........ 4>.......... ,_

_.o=o._oo =o._o _.o=i.ooo

X/Od : 5-I4 : 7.71 = 10,29

4>--

NERSUREO THEm PROFILES FOR TEST NO. 7, TEST SECTION I, THRIN=CONST. , d : 2Si34 , S/O = 4-00 , H/D = 8100

. , .e 1. TemSv_ O[ST Z/8

CONTOUR l 2 3 4 5 6 7 8

VRLUE 0.0800 0.0750 0.1048 0.1250 0.1500 0.1780 0.8000 0.2800

- z t ._ is " " TRFeI.SVF_OlSr. Z/S t.s 0

MERSUREO THEm CONTOURS FOR TEST NO. 7, TMR[N=CONST, J=2B.3, S18=4.0, H/O=8.0

Figure 24

83
s

CONTOUR i 2 3 4 5

VRLUE 0.0500 0.0750 O.I04B 0-1250 0.1000

im t.o

TRAVERSE OI_T, _S T_VCRSE OZS Z/S

6 q 8

0.1750 0.2000 0.2500

_ oo

- • m_csv_ OIST, Z/S t,_ "

PREOICTEO THETR CONTOURS FOR TEST NO.?, TMRIN=CONST, J=26.34. S/D=4,0, H/D=8.0

S/Od =

X/H = 0.50 X/OJ _.14

( TMflIN T)/( TMRIN-TJ]

HO/OJ = 10,29 VRRTIO = 3-47 TRRTIO = 0-464 OENRRTIO=2,192

XIH = 0/75 X/Od =7.71 X/H = 1.00 X/OJ =10.29

h

{TM61N T)/(TMRIN-TJ] (TMQIN-T]/(TMRIN-TJ)

TMQIN = 651.4 K TJET = 302,1 H

X/H = 1-50 Xlnd =15.43

°rm °i_ oi®

[TMATN-T)/(TMRIN-TJJ

THEB = 0,I05

XIH = 2.00 XlOJ _0.57

h

{TaRIN-T)I[TMRIN TJ}

Figure 25

CONPRRISON BETNEEN ORTR RND CORRELRTIONS FOR TEST NO. 7, TEST SECTION I ,UNIFORM TMRIN, J = 26.34 , 5/0 =4.00 , H/O =8.00 84
8 = 0.0508 METERS 81OJ = 5.143 RO/OJ = 10.285 VMR[N = 15.1 M/SEC VJET = 104.1 M/SEC TMRIN = 649,2 R TJET = E98,7 K THEB = O.tSOB BLORRT= 14.868 DENRRTIO= 2.303 TRRTIO=0.460

_ _"_"z,m_" "_ " _" " " 3>......... " 3>......... .... _ _,:.... _ " _' ....

& &- & &

: _,000

, 0s:$1oo o °2°.,7

MERSURED THETR PROFILES FOR TEST NO. 8. TEST SECTION I, THIqlN=CONST. , J : 108.9"7 , S/D - 4.00 , H/D : 8,00

CONTOUR 1 2 3 4 5 6 7 B

VRLUE O.05DO 0.0750 0.1000 0,1250 0.1BOg O,ZO00 0.2_50 0.2400

-o,B Tm_ee_ OlST, _S 1. L.D TR_V_ O[ST Z/S t.O . Zp.AN_SE OZST, Z/8 . _.0 * 5

MERSURED THETR CONTOURS FOR TEST NO. 8, TMnIN:CONST, J:109.0, S/8:4.0, HID:8.0

Figure 26

85
CONTOUR 1 2 3 4 fi 6 7 8

VRLUE 0.0500 0.0780 0.1000 0.1280 0.1808 0.2000 0.2280 0.2400

t.o t.o

• . . . . •s _.5 I_NBV_SE OIST. _S

PREDICTED THETR CONTOURS FOR TEST NO,8. TMAIN=CONST, d=IO£.O, $/D=4.0, H/D=8.0

o.o

1.o

8/OJ = 5.t4 HOIDJ = 10.29 VRRTIO = 6.88 TRRTIO = 0.460 OENRATIO=2.303 TMRIN = 649.2 6 TJET = 298.7 K

X/H = 0.50 X/OJ ::5.t4 X/H = 0.75 X/DJ =7.71 X/H = 1.00 X/DJ =I0.29 X/H = 1.26 X/DJ =12.86

°.= o;w =,_

(TMRIN-T)/(TMRIN-TJ)

=-

F, °I {THRIN-TI/(TMRIN-TJ) (TMRIN-T}/(TMBIN-TJ) [TMRIN-T]/(TMAIN_TJ)

THEB = 0.18t

X/H = 2.D0 X/DJ _0.67

=,w =.= ,_

i,

Figure 27

COHFRRISDN BETNEEN DRTR RND CORRELATIONS FOR TEST NO. 8, TEST SECTION I ,UNIFORM TMRIN, J = 108.97 , S/O =4.00 , N/D =8.00 86
8 =0.0508 METERS S/OJ = 2.561 HO/DJ = 5-121 VNRIN = 15,4 tl/SEC VJET = _09.4 M/SEC TtIRIN = 305.8 1_ TJET = 511.5 K THEB = 0,1830 8LORIqT= 3-765 DENRRTIO= 0.61'7 TRRTIO=I.673

X/HO = 0.500 X/HO = 0.750 X/HO = 1.000 X/HO = 1.5OO = 2.000

/DJ Z._6 X/OJ = 3,84 X/OJ = 6.{Z " X/OJ = 7,68 I0,24

" r

MERSURED THETR PROFILES FOR TEST NO. 9, TEST SECTION I, TMRIN=CONST. , J =31.00 , S/O = 2.00 , H/O = 4,00

CONTOUR

VALUE

I 2 3 4 5 6 '7 B S ID 11

0.0500 0.1000 0.1500 0.1830 0.2000 0.2500 0,3018 0.3000 0.4000 0.4500 0.5000

-_.s , . l,o . TRRNSVERSE0181,Z/5 -5 $" -.0B TRP.NSV£RBEOIST,Z/S I._ I.0 _ . , . 10.

MEQSUREO THETA CONTOURS FOR TEST NO. 9, TNAIN=CONST, J=31.O, S/D-2.0, HID=4.0

Figure 28

87
CONTOUR 1 2 3 4 5 6 7 8 0 10 11

VALUE 0,0500 0,1000 0,1500 0.1830 0,2000 0.2500 0.3018 0.3500 0.4000 0,4S00 0.5000

PREDICTEO THEIR CONTOURS FOR TEST NO.9, IM£IN=CONST, J=31,O, S/O=Z.O, H/O=4.0

8/OJ = Z.55 HO/DJ = 5.12 VRATIO = 7.09 TRAT[O = 1.873 DENRATIO=O.BV/ TMAIN = 305.8 K TJET = 511.5 P{

X/H = D.SO X/DJ _,5(_ X/R = 0.75 x/oJ 3.84

8

(U'IRIN-TI/(THFJIN-TJJ

X/H = [.00 ;(/0,1:=5.[Z

( TtIa IN- ]"J/C TMRIN-TJ J

XA_ = I._o x/oJ =7.68

%

o.® Q.= o_ e.w °_ _:®

CI-R8IN- rJlCTM_ IN-TJ ]

IRES = 0.183

XIH = _.OO X/OJ =i0._4

8t o_ o_ o,

o,

(UiRIN-T]/( TMRIN-TJ]

CDHPRRISON BETWEEN DRTR RND CORRELRTIONS FOR TEST NO. £. TEST SECTION I ,UN/FOR_ T_IN, d = 31.00 , S/O :2.00 , H/O :4.00

Figure 29

88
8 =0-1016 METERS 0/0J = 5.165 HO/DJ = 5-165 VMAIN = 15-2 M/SEE VJET : 103,3 M/$EC [MAIN : 293-5 K TJ_T = 406-1 K TREB = 0.1024 BLORRT= 3.673 OENRBT[O= 0.663 TMA[IG=l.560

&____:y &-- &-- &.--

x,.o0600 x.... o7Ao o _;aOj:lTg _ 8 X/DJ 3.87 ' = "

MEASURED THEm PROFILES FOR TE5T NO. 10, TEST SECTION [, THAIN=CONST. , J =30.64 , S/O : 4,00 , H/O = 4.00

CONTOUR 1 g 3 4 5 6 7 8 9 10 11

VALUE 0.0500 0.1024 0.1500 0,2000 0,2500 0.3018 0.3500 0.4000 0.4500 0.5000 0.5500

m_v£_ OlSr z/s 1.o . T_W_E O_6T, Z/S . t. TF_r_ D_ST Z/$

MEASURED THETA CONTOURS FOR TEST NO.IO, TMAIN=CONST, J=30.64, 818=4-0, HIO=4.0

Figure 30

89
CONTOUR 1 2 3 4 5 6 "7 8 9 10 1I

VALUE 0-0500 0.1024 0.1500 0.2000 0-2500 0.3018 0.3500 0.4000 0.4500 0.5000 0.5500

_._ Tl_t_vo_s¢ OlST . z/s L.s .o

°i ili °i

.o o o.s . l.s .o

PREOICTEO THETA CONTOURS FOR TEST NO.IO, TNRIN=CONST, J=30.6, 5/0=4.0, H/0=4.0

%_ o;. o#

\

SlOd = 5.1"/ HO/OJ = 5.17 VRQTIO = 6.80 TRQTIO = 1.560 OENRQTIO=O.663 TMRIN = 293.0 K TJET = 45"/.2 K THEO = 0,102

X/H = 0.75 X/OJ --3.87

o.= ._ o=

=

X/H = t.oo X/OJ _.t7

%

X/H = 1.50 X/DJ =7.75 X/H = 2.00 X/OJ =10.33

o.® _ °= 0.= °.® ,.®

[TMRIN=T)/(TMAIN-TJ) [T_RIN-T]/(TMRIN-TJ] (TMRIN-T]/(TMRIN-TJ) (TMRIN-T)/[TMRIN-TJ) (TMAIN-T)/(TMRIN-TJ)

CONPRRISON BETWEEN DRTR AND CORRELATIONS FOR TEST NO, 10, TEST SECTION I ,UNIFORB TWAIN, J = 30.64 , S/0 =4.00 , H/O =4.00

Figure 31

90
S : 0.0254 METERS 810J = 2.582 HO/OJ - 10.327 VNAIN = I0.2 MISEC VJET = 102.2 MISEC TMAIN : 29O.3 K TJET 444.8 K THEB - 0.I025 BLORRT- 3,875 DCNRATIO- O.672 TRRTIO-1.532

X/OJ x............... : 0.19 X/OJ o7:_............... X/OJ =I0.35 X/OJ =15.52 x,o,=2o.o6

MEASURED THETA PROFILES FOR TEST NO. 11, TEST SECTION T, TMRIN=CONST , d =30.19 , S/D = 2.00 , H/D = 8-00

CONTOUR I 2 3

VALUE 0.0500 0.1025 0.1500

o 5 T_ OIST, _S TR_Sg DI6T* Z/5

4 5 O 7 8 O 10 tl

0,2000 0.2500 0.3000 0,3500 0.4000 0.5000 0,6000 0//000

s 4.s .

TRAN_ER_ OIST. _/S TR_eWR_ MST, _S

MERSURED THETFI CONTOURS FOR TE_T NO.If, TMIqlN=CONST, J=30.19, S/B=2.0. H/0=8,0

Figure 32

91
CONTOUR I 2 3 4 5 8 7 8 9 I0 It VALUE0.05000.10250.1500O.ZO00 0,25000.30000.35000.40000.50000,80000.7000

1,o t.o 1.o -o.s t.!ill-o,s

_sv_ OIST. _S mq_ OIST. _S Tm_mV_SEOIS_.Z/S

PREDICTED THETR CONTOURB FOR TEBT NO. ii. THRIN=CONST. J=30.19, $/0=2.0 H/O=8.0

1.s ,o

8/OJ = Z.58 HO/DJ = 10.33 VRRTIO = 8,70 TRATIO = 1,532 DENRBTlO=O.67_ Ti!.QIN = 290,3 K TJET = 444,8 K THE8 = O.tOZ

X/H = 0.50 X/OJ =6.10

o= ,.e t_ ,.w =.u :.®

ITMRIN-TI/{TMAIN-TJ)

IVH : 0.75 x/oJ =7.77

=

X/H = t,O0 X/OJ =10.35

°.= a._ ,.=

o'.= o'._ o_ o.m ,= o.® o'._ ,_ o'.® o_ L_

( THRIN-T )/{THRIN-TJ 1 (THRIN-T)/I TMRIN-TJ )

X/N = 1.00 X/DJ =lB.5Z

a

X/H = 2.00 x/oJ _0,S0

D.= p_ =.=

i-)

z"

[TMAIN-T)/{T_RIN-TJ) [TMRIN-T)/ITMRIN-TJ)

COMPARISON BETWEEN DATA AND CORRELATIONS FOR TEST NO, ii, TEST SECTION I, UNIFORM TMAIN, J = 30,19 , B/D =2,00 , H/O =B.O0

Figure 33

92
S =0.0908 NETER5 9/OJ : 4.991 HOIOJ = 9.921 VNRIN : 19.3 N/SEC VJET = 97.6 N/ZEC TNAIN = Z93.O K IJEI = 497.2 K THEB = 0.0617 BLORAT: 4.117 9ENRATIO: 0.747 TROT[O=I.391

XIHO = 0.500 XIHO = 0-750....... X/HO = t.O00 t ii1"X/NO = ..... 1.500 X/HO = 2.000

X/Od 4,96 X/DJ 7.44 X/DJ 9.92 X/OJ 14.88 = X/OJ = _9.84

MEASURED THETR PROFILES FOR TEST NO. 12, TEST SECTION I, TNIqIN=CONST. , J = 30.53 • S/O = 4.00 , H/D = 8.00

CONTOUR 1 2 3

VALUE 0.0250 0.0500 0.0617

_._ --- ,.°. ,.o

TR_R_ 016_ Z S

4 5 6 q

0,0750 0.1000 0.t250 0,1500

8 9 10 11

0.1750 0.2000 0-2250 0-2500

t.o t .a

MEIqSUREO THETFI CONTOURS FOR TEST NO.12, TMAIN=CONST, J=30.53, S/D=4.0, H/O=8.0

Figure 34

93
CONTOUR 1 2 3

VALUE 0.0250 0.0500 O.OBtq

-o._ m_SVERSE DIST, ZlS 1.5 t .o i.o

4 5 6 q

0.0750 O-lO00 0,1250 O-tSO0

8 9 tO It

0.1750 0-2000 0.2250 0.2500

4.5 TR_Vg_S_ olsr. z/s ,.s t.

PREOICTEO THETR CONTOURS FOR TEST N0.12, TMRIN=CONST. J=30.5, S/D=4.0, H/D=8.0

5/oJ =

x/N = o.so x/od =4.96

.>

%

ETMAIN-T)/ITM@IN-TJ)

HO/OJ = 9.92 VRRTIO = 6.39

X/H = 0.95 X/Od=g.44

[TMRIN-T]/ITMRIN-TJJ

TR_TIO = 1.891 OENRRTIO= 0.747

X/H = 1.00 X/Od_,AZ

o.® ._ _._ o._ °_ ,_

(TMfllN-T]/(TMfllN-TJ)

TMRIN : 293.5 K TJET : 408.1K

X/H : 1.50 XIDJ -t4.BB

°_ _._ o._

h.

(TMAIN-T)/[TMAIN-TJ)

THEB : 0.062

X/H : 2.00 X/OJ :19,B4

°_ :_ ,,_

°.® °.= °._ 0_ o._ _

(TMfllN-TI/[IMRIN TJI

COMPARISON BETHEEN ORTFI FINO CORRELATIONS FOR TEST NO. 12, TEST SECTION I .UNIFORM THIqlN. J = 30.53 . S/D :4.00 , N/O :8.00

Figure 35

94
TEST NO. 13

&+

c3

il• t_ m

B _

e

m

m

m

m

m

a

e

i

[ T_X-T W( TMAX- TJ I

_ go

I:3 m

Be

O.O6

TEST NO. 15

m

m

m

o'._o ot,%E m o'._

I T_"_X-T ]/[ TM,_X-I J }

TEST NO. 17

8 m

,5 m

;Lo,, o

m

m

m

m

m

TflETR

Figure

( TtlFIX-T ]It TPI£X-TJ _

36. Profiled

Set ies 2

,,'._ ,:®

Mainstream Theta

Test Cases.

TEST NO. 14

m

e9

,-8-

O.O8 o,_g 0,4_0 e r,_,O

THETR

IT_qX-T )I{ TrliqX-TJ }

TEST NO. 16

i

O,B8

,m

m

m

m

m

m

m

oT,o Z_

m

e_

m

THETtq

I TII_X-T _I { TPIRX-T J

E

m#

ei o

L

TEST NO. 18

m

m

m

o._aTHEl, q o,ee

( TIII:IX_ T J/[ TrlBX_TJ ;

m

m

e

Distributions Used in

95
S =0.0508 METERS 8/OJ = 2,561 HO/DJ = 5-122 VMRIN = t6.9 M/SEC VJET : 59.7 M/SEC TMRIN : 524.4 K TJET = 293,5 K THEB = 0.3120 BLORAT= 7,626 OENR£TI8= 1,805 TR£TIO=0.560

NERSUREO THETFI PROFILE6 FOR TEST NO, 13, TEST SECTION II, TOP COLD , J =22.63 , SI0 = 2.00 , H/D = 4.00

CONTOUR 1 2 3

VRLUE 0,0500 0.1000 0.1500

TRRNSV_SE OIST z s i.o T_YERSE O[ST _S I._

4 5 6 ? 8 9 10 11

0.2000 0.2500 0.3120 O ,3500 0.4000 O.SO00 0.6000 O .7000

-o.s TRp_SVERSEDIST, Z/8 ._ ,o T_NSV_SE OIST 7J_ :,o m_ _IST Z/S _.o

MEASURED THETR CONTOURS FOR TEST NO,t3. TOP COLD, J=22._3, 8/0=2,0, H/On4.0

Figure 37

96
CONTOUR I 2 3

VALUE0,05000.i000.15004 B B 70.2000 0.2500 0,3120 0.3500

°°

8 O 10 It

0.4000 0,5000 0.6000 0.7000

PREDICTED THETA CONTOURS FOR TEST NO. 13, TOP COLD, J=22.63, 6/D=2.0, H/0=4.0

z.o

_qN6VERSE OIST Z/8

5/OJ = 2,56

X/H : O.6O X/OJ_.SB

o,= o_ :.w

(TMRX-T]/(TMAX-TJ)

HO/OJ = 5.12 VRRTIO = 3.54

X/H = 0.75 X/Od --3.84

o,w o= ==

o.® o_ °= == °.= =.®

[TMRX-T)fITMRX-TJ)

TRRTIO = 0.580 OENRRTIO= 1.805

X/H = t.OO X/DJ _.12

o= u,= =.s

i-s_

(TMAX-T)I[TNRX-TJ]

TlllqlN = 52&.4 K TJET = 253,5 K

X/H = 1.50 X/OJ -'dT,B8

ie

o.® °.= o._ == o= ,=

{TMRX-T)I{TMAX-TJ)

THEB = 0.t55

X/H = 2.00 X/OJ =10.24

°,= o.e =u

o= o= °._ °= o,® ,.®

(TMRX-T)/(TMRX-TJJ

COMPARISON BETWEEN B£T_ AND CORRELDTIONS FOR TEST NO. 13. TEST SECTION II, TOP COLD , J = 22.63 • S/D =2.00 , HID =4.00

Figure 38

97
S =0,1016 METERS S/OJ = 4.845 HO/DJ = 4.845 VHA[N = 15.4 ff/$EC VJET = 28,4 M/SEC TMAIN = 672.3 K TJET = 304.7 K THE8 = 0.t140 BLORRT= 3.84? DENRRTIO= 8,210 TRRTIO=0.453

HERSURED THETFI PROFILES FOR TEST NO. 14, TEST SECTION I, TOP COLD , J =7.50 , S/D = 4.00 , H/O = 4.00

CONTOUR 1 2 3

VRLUE 0.0500 0.1140 0.1500

t.o

4 5 6 7 8 9 [0 11

0.2000 0,2500 0.3000 0.3500 0.4000 0.5000 0.0000 0.7000

-" TR_e'_R_ OIST,_S 1. t. Tr_S_R_ OIST Z/S _.0 - ' TR_V_Sg DIST, Z/S _._ t.O

NERSURED THETR CONTOURS FOR TEST NO.14, TOP COLD, d=?,50, S/O=4.O, H/O=4.0

Figure 39

98
I_NSVERSE OIST Z/8

CONT OUR t 2 3 4 5 6 ? 8 9 10 11

VALUE 0.0500 0.1140 0.1500 0.2000 0.2500 0.3000 0.3500 0,4000 0.5000 0.6000 O.qO00

o _ R 0.o

i.o

. _. , •

t.o _'_ _'_ rRBNSVERS£ OIST. Z/8 0 B "tff_t_ B_ _IB

TP.qN6V{RSEOIST Z/_

PREDICTED THETR CONTOURS FOR TEST NO. 14, TOP COLD, J=7.50, S/D=4.O, H/D=4.O

s/OJ = 4.84

XIH = 0.50 X/OJ _.42

o.= o,_ o,®

/

_o •

{TMRX=T)/[TNRX-TJ)

HO/OJ = 4-84

XIH = 0.75 X/DJ _.63

oi_ pF_ D_®

(TMAX-T )/[ TMRX-TJ )

Xl_i = % ,{I0 XIOJ =4.84

:/

_.®

{TMAX-T ]/( TMRX-TJ )

VRATIO = i .04 TRRT10 = 0.483 8ENR_TIG=_.ZIO TMR[N = 6q_.3 K TJET = 304.7 K

X/H = t.50 X/OJ =?.8?

"/

--_._ °:_ o'._ o.. ,'.®

ETMRX-T )/t TMRX-_5 )

THEB = 0-084

X/H : 2.00 X/OJ _.69

o'= o'._ o'.m ,'.. ,'.®

( TM_X-T I/( T_IRX-TJ ]

, SID =4.00 , HID =4.00

COMPARISON BETNEEN DRTR AND CDRRELRTIONS FOR lEST NO. 14, TEST SECTION I, TOP COLO . d = 7,50 Figure 40

99
8 =0.0254 HETERS 8/OJ = 2.688 HO/DJ = 10.353 VMAIN = 15.5 ff/SEC VJET = [09.3 M/$EC TItAIN = 616.1 K T JET = 297.2 K THEB = 0.3029 8LORAT= t4.821 OENRATIO= 2.216 TRATIO=0.482

' " " "_" _:E>_--- ' ........ " - IRE> _" '; "_ " "

_"°: I:I° F -:-_:_F _;II:--I;°.II II I_°._°,

IEISUREI THETt PROFILES FOR TEST NO- 15. TEST SECTION I. TOP COLD . d : 109.1f . I/O = 2.00 . HID = B.O0

4. , .s

CONTOUR 1 2 3 4 6 O 7

VRLUE O.OBO0 0.1000 0.[500 0.2000 0.2500 0.30_ 0.3500

ME_SUREB THET_ CONTOURS FOR TEST NO.15. TOP COLO, J=I09.9. S/O=2.0. H/B=8.O

8 0 10 11

0.4000 0 -5000 0.6000 0.7000

Figure 41

i00
-_.s

CONTOUR

VRLUE

1 2 3 4 5 B 7 8 9 10 11

0.0500 0.1000 0.1500 0,2000 0,Z500 0.3029 0.3500 0.4000 0-5000 0.6000 0,7000

i.o l,e -.o s x. s _.o -o.e

te_ewr_ olot. _/e Te_SVEe_ OZSt. _S

PREOICTEO THETR CONTOURS FOR TEST NO. 15, TOP COLD, J=109.£, 8/0=2.0 H/O=8.0

6/0J = 2,59 HO/DJ = t0,35 VRATIO = %04 TRRTI6 = 0.482 OENRRTIO=2.215 TMRIN = 616.l K ?JET = 297.2 K

XIH = 0.50 XlOJ _-Z8

:/

#-

XIH = 0,76 X/OJ_.76

@° "_= :t= %®

/#.

®

X/H = t.O0 X/OJ =t0.36

:/ ./_,.

( TMRX-T )/( TMRX-TJ ) ( TMAX-T )/( TMRX-TJ ) ( TMRX-T )/[ TilRX-TJ )

XIH : 1,50 X/OJ =16.53

°.= o._ 0=

THEB = O,ZZ3

XIH = 2.00 XlOJ_O.71

=-

_= °.= o_ ,.® o= ,._ o.= °.= o._ o._ o._ ,=

_TMRX-TI/(TMRX-TJ) _TMRX-TJ/(TMRX-TJ_

COMPRRISON BETNEEN ORTR RND CORRELRTIONS FOR TEST NO. [5, TEST SECTION I, TOP COLD • d = 109,85 , S/D =2.00 , H/O =8,00

Figure 42

I01
8 =0.0508 METERS 8/Od = 4.888 HOIDJ = 9.T76 VHRIN = 18.1 MISEC VJET = 68.0 H/GEC THAIN = 58"/.1 K TJET = 310.8 K THEB = 0-0998 8LORQT= 6,908 BENRATIO= 1.856 TRATIO=O,548

&---ie.... & ......... 8>---_

,y, X/HO = 0.500 X/HO = 0.750 0 X/HO = 1.500 = Z.OOO ,.°.=48_ =.88 .,°, .. 1o,,

I.l_ . . . =

- . _ _'_ _

MEASURED THETA PROFILES FOR TEST NO. 16, TEST SECTION I, TOP COLD , J = 22.55 , S/D = 4.00 , H/O = 8.00

C0NTOUR 1 2 3

VALUE 0.0500 0.0996 0.1500

NR_6E 01SI _S I TRN_6£ 016T _$ 0

4 5 6 7

0.2000 0.2500 0.3000 0.3500

1,o

r_v_sE oisT. z/s

8 9 10 11

0.4000 0.5000 0 -6000 0.7000

rR_'_VERSE OIST _/S I 0 _.s TR_S_R_ OIST, 7J8 _'_

HEASUREO THETA CONTOURS FOR TEST NO.16, TOP COLO, J=22.55, 8/0=4.0, H/O=8.0

Figure 43

102
CONTOUR i 2 3 4 5 ? 8 A !0 it VALUE0.05000.099G0,15000,20001.2500,30000.35000,40000-50000-6000O-?OOO

-o. m_SVERSE OIST, Z/S t, t. . m_SV_R_ _IST, Z/S 1._ 1.O _,5 _ 1._ to _ o -O._ , -

PREOICTEO THETA CONTOURS FOR TEST NO. !6, TOP COLD, J:22.55, O/0=4.0 H/D=8.D

0/0J = 4.89 HO/DJ = 9.'78 WtRT[O = 3.49 TRRTIO = 0.548 OENRRTIO= 1,856 TNfllN = 55"7,1 K TJET = 0[0.6 K THEB = 0.053

X/H - 0,50 X/OJ _,89

J

_-.x<_<

[TMRX-T_/[TMRX-TJ]

X/H = 0 ."75 X/Od -'/.33 XIH = 1.00 X/OJ _ .?8

/

_. _ ®

I% 1

_TMRX-T]/I TMnX-TJI [ TtlAX -rl,/[ TMRX-TJI

X/H : ! ,50 X/OJ :14.66 XIH = 2.00 x!oJ =19.55

// ,

(THRX T)/( TMRX-TJ ] ( TMRX-T l/[ TMRX-TJ]

COMPARISON OETNEEN DATA RND CORRELATIONS FOR TEST NO- 16, TEST SECTION I, TOP COLD , d : 22.55 , S/D :4.00 , H/D :8.00

Figure 44

103
$=0.0508 METERS $/Dd=2.434HO/OJ =4.859VMRIN =16,5HISEC V JET = 57.9 M/SEC TRAIN = 538.2 K TJET = 303,3 K THEB = 0.3052 BLORRT= 6,629 DENRRTIO= 1,798 TRATIO: 0.564

,..... . o o1.,_ 5o,

....

ov

....

_0 , .... : OoO : oo

MEASURED THETFI PROFILES FOR TEST NO. 17, TEST SECTION I, TOP HOT • J =22.14 , S/O = 2.00 , H/D = 4.00

CONTOUR i 2 3

VRLUE 0.0500 0.I000 0.1500

o o .o

4 5 6 7 8 9 I0 II

0.2000 0,2500 0.3052 0.3500 0,4000 0.5000 0,6000 0,7000

_.s ]_vER6 £ OIST. Z/B " "0 . _£ OlSr, _$ " 'D

MEASURED THETA CONTOUR8 FOR TEST N0.17, TOP HOT, J=2_.14, 8/0=2.0, H/D=4.0

Figure 45

104
CONTOUR VALUE

o.o

o

2t. o

TP,AP_cR_ OISr _8

1 2 3 4 5 0 ? 8 9 10 11

0.0500 0.1000 0.1500 0.2000 0.2500 0-3052 0.3500 0.4000 0.5000 0.6000 0.7000

I°° !

o

TRRN6YZR_£DIST, Z/S

PREDICTED THETA CONTOURS FOR TEST NO. 17, TOP HOT, J=22,14, StD=2.0 HID=4,O

8/OJ = 2.48

XIH = 0,50 X/OJ =:t.43

__ "

(TMRX-T)/(THAX-TJ)

HO/DJ = 4.87

X/H = 0.75 X/OJ=3.TB

_TMAX_T]/(TMAX-TJ)

VRRTIO = 3.51 TRRTIO = 0.564 DENRRT[O= 1,798 TtIRIN = 538.Z H TJET = 303.3 5

I;

iIX/H = t,50 XIOJ =7.30

o.® o'.= o:w ¢._ o',_ ,',= o_ ,.. ,.. D,m o,m ,:.

I TrIQX-T )/( TMRX-TJ ) {TMAX-T )/(TMRX-TJ)

THEB = 0,153

X/H = 2.00 X/_ _.74

%= %_ %®

(TMAX-T ]/(TMgX-TJ)

COMPRRISON BETWEEN DRTR AND CORRELRTIOND FOR TEST NO. 17, TEST DECTION I, TOP HOT • d = 22.14 , S/O =2.00 , H/O =4.00

Figure 46

105
S =0.0508 METERS S/OJ = 4.869 HO/OJ : 9.737 VMAIN = 18.2 M/OEC VJET - 72.2 MISEC TMRIN = 545.{] K TJET = 3tB.8 K THEB = {].I056 BLORAT= 7.207 DENR_TI{]= 1.757 TR_TI{] 0.581

o = . _ = .

NERSUREO THETR PROFILES FOR TEST NO. 18, TEST SECTION I, TOP HOT , d = 27.69 , S/O = 4.00 • H/D = 8.00

CONTOUR 1 2 3 4 5 6 7 8 9 10 t I

VRLUE 0-0500 0-1060 0.1500 0,2000 0,2500 0,3000 0-3500 0.4000 0,5000 0.6000 0.7000

;, ,_' oo (' ' J' oo '_ ' _ o.o --- _' ; ' ; _' i ili 

mr_s_sE D_ST z/s mnN6VERS[ PInT Z/S T_NSVERSE OIST Z/S

NERSUREU THETR CONTOURS FOR TEST NO.t8, TOP HOT, J=27.69, 8/0=4.0, H/0=8,0

Figure 47

106
CONTOUR l 2 3 4 5 6 7 8 9 iO 11

VALUE0.05000.10660.15000.20000,_5000-30000.35000.40000-50000.60000,7000

; ; o.o ; ; oo i i °.0 i _ -o.o _ I oo

i o .o .o

.o -o.s T_ OtS_. _/S .s " 4 _ Te_SlEeSE OIST Z/S I 6 mAwsveesc ozsT z/s -o.e Te_.s_g OIST, _S '

PREDICTED THETR CONTOURS FOR TEST NOI 18, TOP HOT, Jm27.G9, S/Dr4.0 H/D=8.0

8/Bd = 4.87

x/fl = 0.50 X/Od _.07

%' :"

[TMAX-T}I[TNAX-TJ}

HO/DJ = 9,74

X/H = 0.75 XlOJ =7.30

VRATIO = 3-97 TRQTIO = 0,581 DENRATIO= 1.757 TMAIN = 545.0 K T JET = 316.0 K

X/H = 1.0o x/od _.74 X/H = t,50 X/OJ =t4.61

i

[TMAX-T}I[TMAX-TJ} [TMRX-T]/[TMAX-TJ}

TREB = 0-053

X/H = 2.00 X/OJ =t0.47

[ TMAX-T I/[ mRX-TJ _ _TMAX-T l/( TN_X-TJ )

COMPRRISON BETWEEN BRTR RNO CORRELRTIONS FOR TEST NO. 18, TEST SECTION I, TOP HOT . d = 27.69 , S/0 =4.00 . HID =8.00

Figure 48

107
S =0.0508 METERS S/OJ = 4.051 HO/OJ = 9.021 VNRIN = 15.9 M/SEC V JET - 68.1 N/SEC

×,HO = 0.250 X/HO = 0.500

_ X, DJ = 2.48 X, OJ = 4.96

MERSURED THETR PROFILES FOR TEST NO. 19, TEST SECTION II, TMRIN-CONST- , J - 27.09

TMAIN = 656.2 K TJET - 330.4 K THEB = 0.1055 BLORAT- ?.390 OENRR[[O= 2.020

X_HO = l-O00 X/HO = 2.OOO

X/DJ = 0.92 X/BJ = 19.84

, S/0 - 4.00 , H/D = 8.00

CONTOUR

VRLUE

1 2 3

O.OSO0 0.1055 0.i500

io

-o.s , , 1._

4 5 5 7 8

0.2000 0-2500 0-3000 0.3500 0.4000

, _ _ .o

• T_NSVE_,_" OIST. Z/S 1. 1.0

9 tO

0.5000 0.6000

i o-o

-o.s _._ _'°

MEASUREO THEm CONTOUR5 FOR TEST NO.18, TMAIN=CONST, J=27.09. S/D=4.0, H/D=8.0

Figure 49

I08
TR_V_Se DIST Z S

CONTOUR 1 2 3 4

VALUE 0-0500 0.1055 0.I500 0.2000

4.s m_s_E_sg Dist. _,s i.s 1.o

5 6 ? 8

0.2500 0.3000 0.3500 0.4000

9 I0

0.5000 O .6000

- • m_ , , i.s

PREDICTED THETA CONTOURS FOR TEST N0.I9, TMRIN=CONST, J=Rq.O£, S/O=4.0, H/D=8.0

8/Od = 4.90

X,H = 0.25 X/DJ _.48

4,

_.L , , '_ o® ,®

{ TMAIN T)/[TMRIN-TJ)

HO/OJ = 9.92 VRRT[O - 3.66

X/H : 0.50 X, OJ -_.£6

[TMQZN-T_/(TMOIN-TJ)

DENRRTIO=2.020 TMQ[N = 666.2 K

X/H - t.O0 X/OJ _.£2

_.m o._ o._

i)

[TMRIN-T)I( TMn[N-TJ 1

TJET = 330.4 K THEB = 0-106

X/H = 2.00 X/Od =1£.B4

o.® o.,o _._ °_ o.m ,.,

ITMn:N T)/(TNRIN-TJI

COMRQRISON OETNEEN OQTR ONO CORRELATIONS FOR TEST NO- 19, TEST SECTION II,UNIFORM TMQIN, d = 2710£ , _/0 24"00 , H/D -8,00

Figure 50

109
$ = 0.0508 METERS

X/HO = 8,260

X/DJ = 2.52

S/OJ = 5.037 HO/DJ = 10.074 VMAIN = 15.5 M/SEC VJET = t06.4 N/SEC TMRIN = 644.6 K T JET = 3i3.£ K THEB - 0.L881 BLORRT= t5.278 OENRATIO= 2.L85

-_&- _ ---_--'°

aoD X/HO = 0.500 = t.O00

- lo.o7

MEASURED THETFI PROFILES FOR TEST NO. 20, TEST SECTION II . TH/qIN=CONST. , d = 102.50 . S/O = 4.00 . H/O = 8.00

_o.o

TR_SVF_SE OIST. Z,'S

CONTOUR l 2 3

VRLUE 0.0500 O. 1000 O. 1500

-o.s . , i,s

4

0.1881

5 6 7 8 0 [0

0.2000 0.2500 0.3000 0-3500 0-4000 0-5000

-e.s ,s o.s 1.6 TR_e_ oisT. z_s TR_E_SEO[_T.Z/8

NERSUREO THETR CONTOURS FOR TEST NO.20. TNRIN=CONST. J=102.5. S/0=4.0. H/O=8.O

Figure 51

ii0
CONTOUR l 2 3 4

VFqLUE 0-0500 0-I000 0-1500 0-i881

i 1 lB. _

5 6 '7 8

0 -2000 O -2500 0.3GO0 0.3500

.s TRQNSVE_SE_IST. LS l, Z,_

£ tO

0.4000 0.5000

°°;

_ TRO_SVERSE DIST _S

PREOICTED THETFI CONTOURS FOR TEST NO.20. TMIqIN=CONST, J=102.5, S/B=4.0, H/D=8.0

S/DJ = 5.04

X/H = 0.25 XzDO _,SZ

® °,5 o_%=

o.m o:= _.,_ o._ °._ ,.®

[ TMR IN-T )/C TMR IN~TJ 1

HO/DJ = 10.07 VRRT[O = 6.85

X/H = O-SO X/Od _.o4

® o,._ o.,o o,.=

o:® o._ °._ o._ o._ ,._

(TMRIN-T )I[ TMAIN-TJ)

TRATIO = 0.487 DENRRTIO=2-185 TMAIN = 644.6 K

X/H = l.O0 X/OJ =10.07

%

(TMA[N-TIlITMRIN-TJ)

TJET = 313.£ K THEB = 0.188

X/H : 2.00 X/OCt0.15

[TMRIN-T)/(TMRIN-TJ)

COMPSRISON BETWEEN DATA AND CORRELATIONS FOR TEST NO- 20, TEST SECTION II ,UNIFORM TMAIN, J = 102.50 , S/O =4.DO , H/'D =8.00

Figure 52

111
0 =0.0508 NETERS

= 2.45

MERSURED THETIq PROFILE8 FOR TEST NO. 21, TEST SECTION If, THFtIN=CONST. , J = 5.75

5/oJ = 2.482 HO/OJ = 4.923 VNflIN = 15.8 M/SEC VJET = 28.1 M/8EC TflRIN = 653.7 K TJET = 307.9 K

_SI_:I:IIO _/II--LII°

• S/0 = 2.00

THEB = 0,1973 BLORRT=8.794 OENRflTIO= 2.129

i_. IIII= l.ooo

= 9.85

H/D = 4.00

CONTOUR t 2 3 4

VRLUE 0.0500 0.I000 0.1500 0-i073

_=_ ---- _.__.o

5 6 7 8

0.2000 0.2500 O.3000 O .3500

TRP.N_VEI_E Ol6r,z,s

9 lO

o .4ooo 0.4503

MEASURE0 THEm CONTOURS FOR TEST NO.21, TNAIN-CONBT, J=6.76, S/0=2.0, H/0=4.0

Figure 53

112
CONTOUR

VALUE

I 2 3

0.0500 0.1000 0.1500

4 5 6 7 8 £ 10

0.[£'73 0.2000 0-2500 0.3000 0.3500 0-4000 0.4500

l.o

PREOICTEO THETR CONTOURS FOR TEST NO.21, TMRIN=CONST, J-6.76, S/D-2.0, H/0-4.0

S/DJ =

X/H = 0.50 X/DJ _.46

_._ _.,_ o._ o._ o._ ,.®

[TMAIN-T]I[TMAIN-TJ]

HO/DJ = 4.9Z VRATIO - 1.78

XM - 0.75 x/OJ _.89

[TM£IN-TJ/(TM£IN TJJ

TRnTIO = 0.471 OENRATIO=2.t_9 TMR[N - 653.7 K

X/H = l.OO ×/BJ _.92

:\

¢

[TMRIN-T 1/[ TMfqlN Td]

TJET - 307.9 K THEO 0-197

X/H = 2.00 ×lOde.85

[TMRIN-T)/ITMRIN-TJ]

COMPARISON BETNEEN DF_TA RNO CORREL.FITION8 FOR TEST NO. 2i, TEST SECTION II.UNIFORM TMOIN, d = 5.76 , S/O -2.00 . H/D =4.00

Figure 54

113
S = 0.0508 METER8 8/OJ : 2.582 HO, BJ = 5,164 VMNIN : 15.8 M/SEC VJET = 04.5 M/SEC TMRIN : 553.7 K TJET : 303.8 K THEB = 0.3074 BLOR£T= 7.538 OENRRT[O= 2,179 TRBT[O=0.465

c2>_

, ×111-7:11°

0.750

/ 0.87

j X/HO = i-O00 X/HO = 2.000

XzOJ = 5.10 X/OJ 10.33

MEASURED THETFI PROFILES FOR TEST NO. 22> TEST SECTIONI[, TMAIN=CONST. , d =26.0? , S/0 = 2.00 , H/D = 4.00

'x--/_ °°

a. T_mVE_SE nZ_T. Z/S t.5 1.O

CONTOUR t 2 3 4

VALUE 0.0500 O-iO00 0.1500 0-2000

m_sw_E ui_T _ _ o

E 6 7 8

0.2500 0.3074 0.3_00 0.4000

_ i I

r_n_r e_sr oE _

9 lO

0.4500 O-E000

T_,_SV_SE II_T, _/s

MEASURED THETS CONTOUR6 FOR TEST N0,22, TMRIN=CON$T, J=26.07, S/B=2.0, H/D=4,0

Figure 55

114
- • TRaNSVErSE OlST, Z/B , I.O

CONTOUR 1 2 3 4

VALUE A.0500 0,1000 0.1500 0.2000

°°

-o._ mANSVERSE OIST, _'_ '

S 6 7 0

0-2500 0 ,3074 0 ,3500 0 ,4000

T_SVE_SE O_ST Z/S

£ 10

0.4500 0,5000

- .s TR_SWSE OIST, _/s 1. _.o

PREBICTEB THETR CONTOURS FOR TEST N0.22, TNAIN=CONST, d=2B.OT, 8/D:2.0, H/O=4.0

$/OJ = Z,EB AO/OJ =5,t6 VRRTIO = 3,46

X/H = 0.50 XIOJ _.58 X/H = 0.75 X/OJ --3,B?

•

f

{TMAIN-TI/ITMRIN-TJ) [TMFIIN TI/{TMAIN TJ]

TRRTIO = 0.465 OENRRTIO=2.179 TWAIN = 653,? I(

X/H = t.O0 X/OJ _.16

s.

( TMA IN-T )/( TMf_IN-TJ )

TJET = 303,8 K THEB = 0.307

X/H = 2,00 X/OJ =10.33

(TMA [N-T )/( TMRIN-TJ )

COMPRRISON BETWEEN OATA QNB CORRELRTIONS FOR TEST NO. 22, TEST BECTION II,UNIFORM THAIN, J = 26.07 , S/O =S,O0 , H/O =4.00

Figure 56

i15
£ =0.0508 METERS $lOJ = 4.925 HO/DJ - 9.85] VMRIN = 17,0 M/SEC V JET = 53,8 M/SEC TMOTN = 945.5 K

x×SH0oj:o = 2.49.... ;;_:::5°03°

MEflSUREO THETA PROFILES FOR TEST NO- 23, TEST SECTION IV, TMRINuCONST , J - 21.07

TJET = 319.2 K THEB = 0,0972 BLOROT= 6.953 DENRRTIO- 2402

4>

50: = .

, S/E) = 4.00 , H/D - 8.00

CONTOUR 1

VRLUE 0.0500

m_vr_ o_sT. z/s

2 3 4 5 O 7 8 0

O.OB?2 0.I500 0.2000 0.2500 0.3000 0.3500 0.4000 0,5000

__L ;

°°

-o.s T ' . . _.o

R_S_ERS_ DIST z/s

I0 11

0.5000 0.7000

__L__ 1 _

i.

T_SV_Se e_sr. _S

MERSUREO THEm CONTOURS FOR TEST N0,23, TMAIN=CONST, J=21.07, S/D=4.0. H/O=8.0

Figure 57

i15
CONTOUR !

VALUE 0.0500

_. . to

T_SVERSE OIST. _S

2 3 4 6 fi ? 8 9

0.0972 0.1500 0.2000 0.2500 0.3000 0.3000 0.4000 0.6000

10 Ii

0 •6000 0.7000

PREDICTED THETR CONTOURS FOR TEST NO. 23, TMRIN=CONST, J=21,O?. SID=4.0 HID=8.0

S/OJ = 4.g3

X/H = 0,_5 x/od _,48

(TMRIN T)/[TNRIN-TJ)

HO/DJ = 9.86 VRATIO = 3.17 TRQTIO = 0,484 DflNRRTIO=2.102

X/H = o,50 X/OJ =4.93

D.® o.=o .._ o.= o._ ,.®

[T_IR IN_T )/( TNRIN-TJ )

TNQIN = 645-5 K TJET = 312.2 H THEB = 0.097

XYH - 1,0o x/oJ _,B5

(TMAIN T 1/( TNR IN-TJ ]

COMPARISON BETHEEN DATA AND CORRELATIONS FOR TEST NO. 23, TEST SECTION IV, TMRIN=CONST, d - 21,07 . S/D =4,00 , H/O =B.O0

Figure 58

i17
5=0.0508 METER@ 8/0J=5.000HO/OJ =10.000 VMFIIN =_5.9M/$ECVJET =I05-I M/SECTMRIN =042.8K

_;-_ ---_.-_

XIHO O.250 XIHO = O.500

_ X/OJ 2,50 " X/OJ = 5-00

MEASUREB THETA PROFILES FOR TEST NO. 24. TEST SECTION IV. TMRIN=CONST , J = 85.84

T JET = 311.0 K THEB = 0.1781 BLORAT- 13.792 DENRRTIO= 2,217

....,x×/Od......

= 10-00ooo

, S/I] = 4,00 , H/D = 8,00

TRRTIO= 0 -4B4

CONTOUR t

VALUE 0-0000

2 3 4 5 6 7 8 9

0.I000 0.1000 0-1781 0-2000 0-2500 0.3000 0.3500 0.4000

tO

0.4500

MERSURED THETR CONTOURS FOR TEST N0.24, TMRIN-CONST, J=85.84, S/D=4.0, H/D=8.O

Figure 59

118
CONTOUR 1

VALUE 0-0500

IR_6WSE DISI, Z,S _.O

2 3 4 5 6 7 8 9

O.lO00 0.1500 0.1781 0.2000 0.2500 0.3000 0.3000 0.4000

10

0.4500

PREDICTED THETR CONTOURS FOR TEST N0.24. TMRIN=CONST. J=85.84, S/D=4.0. H/B=8.0

S/Od =

x/H = o.25 XIDJ _.SO

_"_

[TflAIN_T)/(TNRIN-TJ]

VRRTIO = 6.22 TRRTIO = 0.484 OENRATIO=2.21?

X/H = 0._0 X/Od 2.00

( TMRIN-T I/( TMA IN-TJ )

TMRtN = 64_,8 K TJET = 311,0 K THEB = 0,178

X/H = t.OO X/OJ =tO,O0

i.it

o.® o.= o._ o._ o._ ,_

(TNRIN-T 1/[ TMAIN-TJ]

CONPQRISON BETNEEN ORTR RNO CORRELATIONS FOR TEST NO. 24. TEST SECTION IV.UNIFORN TNRIN, d = 85.84 . S/O =4.00 • H/D =8.00

Figure 60

119
S : 0,0508 METERS G/Dd = 2.538 HO/DJ = 5,075 v_qIN = 15.I M/SEE VJEI = 27,7 M/SEC TMRIN = 643.4 K

(_>-!_/J x/,o = 0,75o

XlOJ = 3,8t

MERSUREOTHETR PROFILES FOR TEST NO. 25, TEST SECTION IV, TNRIN=CONST . d =6.73

TJET = 321.6 K THEO= 0.1830 BLORQT= 3.672 OENRATI8= 2.003

• : _:_o

, S/O = 2.00 , H/O = 4•00

TRRT[O= 0.5O0

CONTOUE t 2 3 4 5 6 7

VRLUE 0.0500 O.tOOO 0.1500 0.t830 0.2000 0.2500 0.3000

4. re,versE OL_T, _/S t.t.o _o_ TILqNSVERS_OIST, _/S t.I.

8 0

0.3500 0 -4000

tO

0.4500

_ oo

-o.s T_SVEeSE ol_T. z,s _"_ L._

MERSUREO THETR CONTOURS FOR TEST N0.25, Tt1OIN:CONST, J=6.73, S/D=2.0, H/0=4.0

Figure 61

120
CONTOUR l

VALUE 0 -0B00

2 3 4 5 6 7 8 9

0-I000 0.1500 0.1830 0-2000 0.2500 0.3000 0.3500 0-4000

iO

0.4500

PREDICTED THET£ CONTOURS FOB TEST N0,25, TNRIN=CONST, J=6.73. S/B=2.0, H/O=4.0

S/Od = 2,54

X/H = 0.60 X/DJ _.54

o.® o.® o._ _ _ ,=

[TMAIN-TJ/[TMRIN-TJ]

VRQTIO : t,83 TRRTIO : 0.500 BENRQTIO=2.003

X/H = 0.75 X/Od _.81

_,"

{TMQIN-TI/ITMRIN-TJI

TMRIN = 643-4 K TJET = 321,6 K THEB = O.1B3

X/H = t.8o x/_ _.08

%'= _ _,_

L.

l-

(..............

ITNRIN-Tl/[TMQIN-TJ}

COMPORISON BETWEEN DRTB RNO CORRELBTIONS FOR TEST NO. 25, TEST SECTION IV,UNIFORM TMRIN, d = 6.73 • SIO =2.00 , H/D =4,00

Figure 62

121
5 : O._OB _IETE,R_ 8ZOJ = _,58_ HO/DJ = _,164 WIRIN : 14,9 M/SEC VdET : _5.1 tl/SEC TtIRIN = 54g,7 K TJET = 3_@,_ ff IHE_ = O.g98B BLO_@_=3.233 OENRRIIO: 1,9_8

MERSURE_ THETR PIiOFILE8 FOR TEST NO. 25, TEST SECTION IV. T,qR_NaCONST • J :26,73 . 8/0 : 2.00 , H/O = 4.00

TRRTIO=O.51_

CONTOUR I 2"

VRLUE 0.0500 0.1000

\ k\// _, _v j _._

3 4 5 6 7 8 O

0.1500 0.2000 0.2500 0,2988 0,3500 0,4000 0.4500 0.5000

10

F---{ ..... -T---3-_ o..,

NERSUREO THETR CONTOURS FOR TEST N0.28. TNRIN=CONBT. J=28.73, 6!0-2.8. U/O=,_,O

Figure 63

122
CONTOUR i

VALUE 0,0500

-0.6 TP_SWR_ OZST. Z.'_ . t.O

2 3 4 5 6 ? 8 9

O.lOOO 0.1000 O.20OO 0.2500 0.2988 0.3500 0-4000 0-4500

-. , t.6 l,o

tO

O .50OO

-o.s TR_NSV_ OIST , z/s _,5

PREDICTED THETA CONTOURS FOR TEST NO.2S, TMRIN=CONST, J=26.73, S/0=2.0, H/D=4,0

S/Od =

X/H = 0.60 X/Od _.58

a.= o.e o._

g.= :=o =._ o.® ,.® ,.®

(TMRIN-T)/[TMRIN-TJ)

2.58 HO/OJ = 5,16 VRRTIO = 3.70 TRAT[O = 0-5t5 OENRRTIO=t.958 TMR[N = 640.7

X/H = 0.75 X/Bd--3.87

[TMRIN-TI/(TMAIN-TJ)

TJET = 329,8 K THEB = 0.2gg

X/H = l.oO x/OJ _.t6

o.® =.= °._ 0.® a.= ,=

(TMRIN-T)/[TMRIN-TJI

COMPARISON BETWEEN OBTB RNO CORRELATIONS FOR TEST NO. 2B, TEST SECTION IV,UNIFORM TMRIN, d = 26.73 , S/D =2,00 , H/O =4.00

Figure 64

123
5 =0.0508 METER5 5/0J = 4.98l HO/OJ = 9.921 VMRIN = 16.1 M/SEC V JET = 58.7 M/SEC TM£[N = 646.4 K TJET = 320.9 K THEB = O.tO65 BLORRT= 7.470 OENRRTIO= 2.053

4>- 6---_- .... ' .... d>--_---_:-- X/HO = 0.500 4>--_1o _ 0

°', -- : ×,oJ: 4.o_

MERSURED THETR PROFILES FOR TEST NO. 2"7, TEST SECTION V, TMRIN=CONST , J =27.18 , S/B = 4.00 , H/D = 8.00

TRRTIO= 0.498

CONTOUR 1

VRLUE 0.0500

_ _

s T_S_R_ OlSr z_

2 3 4 5 5 7 8 0

0.1060 0.t500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500

tO

0.5000

oIC/ ?A i °°

oG _N_ER_ OIS: z/s s

MERSURED THEm CONTOURS FOR TEST N0.27, TMRIN=CONST, J=27.18, 610=4.0, H/O=8.0

Figure 65

124
CONTOUR I

VALUE0.0500

2 3 4 5 6 q 8 9

0.t065 0.1500 0.2000 0.2500 0.3000 0.3500 0-4000 0-4500

tO

0.5000

___ ...... L___

to

T_6_R_ DZDT Z/6 15

PREDICTED THEIR CONTOURS FOR TEST N0.27, TMRIN:CONST. J:27.18, St0=4.0, H/O=8.0

s/oJ = 4.96

XIH = O.Z6 xlOJ _.48

(TMQIN-T)/{THRIN-TJ)

HO/DJ - 9.9Z VRAT[O = 3.64 TRATIO = 0.496 OENRRTTO=Z .053

X/H = 0.50 XIBJ --4.66

8

(THQIN-T)/(TMRIN-TJ)

TffAIN = 646.4 _{ TJET = 9Z0.3 K THEB = 0.107

X/H : 1.00 X/OJ _.Z

.® o_ °., o.®

i-'ii/

BITMAIN-T)/(TMA[N-TJ)

COMPARISON BETWEEN ORTR AND CORRELRTIONS FOR TEST NO. 27. TEST SECTION V,UNIFORM TMAIN, d = 27.18 . S/D =4.00 . H/O -8.00

Figure 66

125
6 = 0.0508 METER8 $/0J = 6._1 HO/OJ = 10.121 TJET = 319.1

ct>

MEASURED THETA PROFILES FOR TEST NO. 28. TEST SECTION V. TMAIN=CONST.. d =i06.72 . S/D = 4.00

VMRIN = 16.0 M/SEC VJET = 112.5 M/SEC TMRIN = 645.1 K K THEB = 0.1888 8LORRT= 15.176 OENRRTIO=-_.159

i X/HO = I.O00

X/OJ = 10,12

, H/D = 8.00

TART[O=0.496

CONTOUR 1 2 3 4 5 6 7

VALUE 0.0500 O.lO00 0.1500 0.1888 0.2500 0.3000 0.3500

o.o o,o

" _qc_v_olsr, _8 . 1,o m_svaucmsr _s

8 9

0.4000 0.4500

tO

0.5000

to

-. . . .

MEASURED THETR CONTOURS FOR TEST N0.28, TMAIN=CONST, J=[06.7, S/O=4.0, HIO=8.0

Figure 67

126
CONTOUR 1 2 3 4 5 6 ? 8 9 10

VALUE 0.0500 0.1000 0.[500 0.1888 0.2500 0.3000 0.3500 0.4000 0.4500 0.5000

-. . . t.o -o,s TUm_ reST, Z/S l,s

, ; _/ i 0o

i

mm_-VESSE OlST Z/S t.o

PREDICTED THETR CONTOURS FOR TEST NO.28. TMRIN=CONBT. J=106.7. S/D=4.0, H/D=8.0

$/DJ = 5.06 HO/DJ = lO.t2 VRRTIO = 7.03 TRRTIO = 0.499 OENRgTIO=2.t59 TMRIN = 645._ K TJET = 9t9.1 K THEB = 0.t89

X/H = O.tS X,/DJ ::_ ,53

|-

{ TMRIN-T )/( TMRIN-TJ ]

X/H = O.BO X/OJ =5.06

( TMAIN-T )/(T_IN-TJ)

X/H : t.o0 x/oJ =10,12

o_ o_ i_ o_ ,m

( TMRIN-T )/{ TMRIN-TJ ]

COMPARISON BETWEEN DRTR RND CORRELRTIONB FOR TEST NO. 28, TEST SECTION V,UNIFORM TMAIN, J = i06.72 , S/D =4.00 , H/D =8.00

Figure 68

127
s = o.o5o8 METERS 610J = 2.462 HO/DJ _ 4.924

._IIIP' x/_o = o.soo

MDqSUREO THETtq PROFILES FOR TEST NO, 26, TEST SECTION V, TMRIN=CONST. , J = 7.0'7

VMFIIN: 15.7 il,/$EC VJET : 29.1 _L/SEC TMRIN = 645.0 K TJET = 313.5 K THEB = 0,1983 BLORRT= 3.BIB DENRRT[O= 2.064

_¢_=°_._ _ 4_°°°._

• S/O = 2.00 • H,/O = 4,00

TR£TIO=O.486

CONTOUR 1 2 3 4 5 6 7

VALUE 0.0500 O.IO00 0-1000 0.1684 0.2500 0.3000 0.3500

, ; _ oo _ _ _ _; _ _o

-o._ . , , . _ s T_'_V_E OISTZ/S "

8 0

0.4000 0.4SO0

1o

o ,5000

; .l oo

-o._ TRF_SV[_Z_IST.z,s .s 1.

MERSUREO THETR CONTOURS FOR TEST N0.29. TMRIN=CONST, J=7.O?, S/0=2.0, H/D=4.0

Figure 69

128
CONTOUR 1

VRLUE 0.0500

_'_ • . i . i.o ?_S_RSE OIST _ S _ S

2 3 4 5 6 '7 8 9

0.I000 0.1500 0.1984 0.2500 0.3000 0.3500 0.4000 0.4500

T_NSVE_SE O[_T _Is S

10

0.5000

PREDICTED THETR CONTOURS FOR TEST N0.29, TMPIN=CONST, J=7.07, S/D=2.O. H/D=4,0

S/DJ = 2.46

X/H = 0.50 X/DJ _.45

(TMRIN-T)/ITtlRIN-TJ)

VROTIO = 1.55 TRSTIO = 0.486 OENRQTIO=2.OB4

X/H = 0.75 X/OJ 4.69

5"

o_ o_ o._ o._ ,_ ,.®

[Tt_qIN-T)/(TMRIN-TJ)

TMRIN = 645.0 6 TJET = 313.5 K THEB = 0.I98

X/ff = 1.00 Xl_J -_.92

[TMRIN-TI/(TMAIN-TJ)

COMPARISON BETHEEN DATA AND CORRELATIONS FOR TEST NO. 29. TEST SECTION V.UNIFORN TNAIN. d = 7.0"7 . S/O =2.00 . R/D =4.00

Figure 70

129
S:0.05O8 METERS S/OJ _ 2,540 HOIOJ = 5.080 VMRIN = 15.6 M/5EC VJEI = 56,4 M/SEC TI_IN = 545.5 K TJET = 313,7 K THEB = 0.3149 BLORRT= q+54g DENRAT[O= 2.08?

<:_. ct> <_

= 2+54 _+ XlOd = 3.81

MEASURED THEm PROFILES FOR TEST NO. 30, TEST SECTION V, TMRIN=CONST. • d = 27.3i • S/O = 2.00 , N/D : 4.00

IRRT[O= 0.486

CONTOUR i

VFILUE 0.0500

o.o

2 3 4 5 6 7 8 9

0.[000 O.ISO0 0.2000 0.2500 0+314£ 0.3500 0.4000 0.4500

k x-/i/ \i ,2°. °

o e TP._r_ERSE OIST Z S I _

tO

0.5000

_i + o+

T 7.8 *

NERSUREO THETR CONTOURS FOR TEST N0.30, TtlRIN=CONST, d=27.gl, SIB:2.0, H/D=4.0

Figure 71

130
CONTOUR £

VALUE 0.0500

1

2 3 4 5 6 7 @ S

O.iO00 0.1500 0.2000 0-2500 0.3149 0-3S00 0.4000 0-4500

• _NSV_RS¢ OlST, Z,S .s t.

10

0.0000

__ o.o

PREOICTED THETR CONTOUR5 FOR TEST NO.30. TNAIN:CONST. J:27.31. 5/0:2.0. H/O:4.0

s/oJ = z .54

x/H = o.5o X/DJ _.fi4

,_ :.o o.,o :._ o_ l.=

{TMBIN-T)/ITMRIN-TJ)

HO/_J = 5.08 VRRTIO = 3.6_ TRATIO = 0.486 OENRATIO=2.087 T_IRIN = 545.5 K

X/H : 0.75 X/oJ _.B[

(TM_IN-TI/(TtIRIN-TJ]

TJET = 313.7 K THEB = 0.31_

X/H = I.OO X/OJ_.OB

(TMRIN-T)/(TMRIN-TJ)

COHP_RISON BETWEEN DATQ QNO CORRELBTIONS FOR TEST NO. 30, TEST SECTION V.UNIFORM TMRIN, J = 27.31 , $/_ :2,00 , H/O :4.00

Figure 72

131
$ = 0,0_508 METERS $10J = 4.941 HO/OJ = 8.883 VMQIN = 1,6.4 MISEC VJET = 58.6 M/SEC TMNIN = 649.2 H TdET = 319.5 K THEB = 0.1066 BLORQT= '7.4_t SENRQTIO: 2.0"/2

_o

NERSUREB THETR PROFILES FOR TEST NO. 31, TEST SECTTON V[, TMRIN=CONST , d --26.59 , ,5/0 = 4.00 , H/D = 8,00

TART[O= 0,492

CONTOUR I 2

VALUE 0.0500 0 I_056

3 4 S 6 7 B 9

0,1250 0.1500 0.2000 0.2500 0.3000 0.3500 0,4000

-o. r_sE PEST. Z/S I.b 1,0

tO

0.4500

_ i .

, .s t,e iR_m_ O_ST Z,S

MEASURED THETR CONTOURS FOR TEST NO.31, TMA[N=CONST, J=26,59, S/0=4.0, H/D=S.O

Figure 73

132
CONTOUR I

VALUE 0.0SO0

2 3 4 5 6 7 8 9

0.1066 0-1260 0-1500 0.2000 0.2500 0.3149 0.3500 0.4000

_.s IR,_VO_SE OIST. _/S .s l.o

10

0.4500

Te_W _ OIST Z/S

PREDICTED THETA CONTOURS FOR TEST NO.3I. TNAIN=CONST. J=2fi.59. 510=4.0. H/O=8.0

S/DJ = 4,s4

X/H = 0.2S XIOJ _,47

_. °,.'"

{TNR IN-T )/[ TMBIN-TJ )

HO/OJ = 9.88 VRRTIO : 3.5B TRRTIO = 0.492 DENRRTIO=2,072

X/H = 0.50 X/OJ :4.S4

o= _ _®

fl).°"

[TiIRIN-T 1/[ TMFIIN-TJ 1

TMRIN = 649.2 K TJET = 319.5 _ THEB = 0,I07

X/M = L.O0 XIDJ _.8B

[TM£1N-T]/[TNRIN-TJI

CONPARISON BETNEEN DATA AND CORRELATION6 FOR TEST NO. 31. TEST SECTION VI.UNIFORN TNAIN. d = 26.59

• 6/0 =4.00 , H/O =8,00

Figure 74

133
$ =0,0S08 METERS S/OJ = 5.0B1 HO/OJ = 10,163 VMAIN = 16,5 M/_EC VJET _ 1Ifi.0 I1/SEC TMAIN = 647,0

MERSUREO THETA PROFILES FOR TEST NO. 32, TEBT SECTION VI, TMRIN=CONST , d = IO?.?G

K THEB = 0,1887 BLORAT= 15,287 OENRnTIO= 2.17S

(_:>-_IIIIIIII_\\\\_(_E> ........ _ X/_O = 1.000

X/DJ = lO.lB

, $/D = 4.00 , H/O = 8.00

TR_TIO=O.496

CONTOUR I 2

VALUE 0.0500 O.lO00

3 4 5 fi 7 8 9

0.1500 0,1888 0.2500 0.3000 0.3500 0.4000 0.4500

, _ o_

10

0.5000

T_N_E_SE ol_ z/s

HEASURED THETB CONTOURS FOR TEST N0.32. THAIN:CONST, J=i07.8, 8/0:4.0, H/O:B.O

Figure 75

134
CONTOUR I

VALUE 0.0500

2 3 4 5 6 ? B 9

0.i000 0.1500 0.1888 0.2500 0,3000 0.3800 0.4000 0.4500

-o, , , , L._ i.a

10

0.5000

r_veese OlST. z/_ "_

PREOICTEO THETR CONTOUR8 FOR TEST N0.32, TNRIN=CONST, J=i07,8, 5/0=4.0, H/O=8.0

$1Od = 5,08

X/H = 0,25 XIBJ_.S4

[TMRIN-T)/(TMRIN-TJ]

HOIOJ = _0.18 VRRTIO = 7.04 TRATIO = 0.496 OENRRTIO=2.1?6 TMRIN = 6&7.0 K

X/H = O.50 X/OJ_.O_

o® o.,, o.,o o_ o.,o ,.®

[TNAIN-T)/(TN_IN-TJ)

TJET = 321,2 K THEB = 0.189

XIH = l,O0 XlOJ =_O.IS

_ °_o o_ o_ o.= ,=

{TMO[N-T)ICTMRIN-TJ)

CONPRRIBON BETNEEN DRTfl RNO CORRELRTIONS FOR TEST NO. 32, TEST SECTION VI,UNIFORN TMRIN. d = i07.75 • 5/0 =4.00 . H/O :S.O0

Figure 76

135
$ :O,OBOB mETERS 8/OJ = _.SOO HO/OJ = B.OOI VMAIN = 16.3 M/SEC VJET = 29.K M/SEC TK_qlN= 649.8 K TJET = 301.3 K THEB = 0.1969 BLORAT= 3,903 DENRATIO= 2.165 TRATIO=0.464

MERSUREO THETR _'ROFILEO FOR TEST NO. 33, TEST SECTION VI. TMRIN=CONST . d = 7.05 , S/O = 2.00 . H/O = 4.00

CONTOUR i 2 3 4 5 6 '7

VALUE 0.0500 0.i000 0.1500 0.1869 0.2500 0.3000 0.3500

8 £

0.4000 0.4500

1o

0.5000

MEASURED THETR CONTOURS FOR TEST N0.33, TNAIN=CONST, J=7.05, S/D=2.0. HID=4.0

Figure 77

136
CONTOUR L

VALUE 0,0500

2 3 4 5 6 '7 8 O

O,tO00 0,1500 0.1969 0.2500 0.3000 0-3_00 0.4000 0,4500

°°

_'_ m_vr_6e OIST, Z;_ _._ *.e

10

O .5000

-o,s _sv_ea_ otsT. z/s . .o

PREOICTED THETA CONTOURS FOR TEST N0.33, TNNIN=CONST, J=?.05. 8/0=2.0, H/O=4.0

S/[3J =

X/H = 0,50 X/DJ _,50

[TM£IN-TI/(TMQIN-TJ)

2.O0 HO/OJ = 5.00 VRnTIO ; 1,80 TRATIO = 0,454 OENRRTIO=2,165

%

(TMRIN-II/ITY_qIN-IJI

TMAIN = 649,8 K TJET : 301.3 K THEB - 0.1£7

X/H = _ ,00 X/OJ _.00

_ °r_

|."

_TMAIN_T_JtTftnIN_T_

COMPARISON BETWEEN OOTB BNO CORRELgTIONS FOR TEST NO, 33, TEST SECTION VI,UNIFORH TMBIN, J : 7,OB

. S/O =2.00 , H/D =4.00

Figure 78

137
$ =0.0508 METERS $/DJ = 2,061 HO/OJ = 5,122 VtllqIN = 16,2 N/SEC V JET = 5S.9 M/SEC [tlAIN = 600.8 K TJET = 290.9 K THEB = 0,3144 BLB_I_T 7.657 DENRRIIO= 2.225

MEIqSUREO THETA PROFILES FOR TEST NO. 34, TEST SECTION VI, TMRIN=CONST . J = 26.40 , 5/0 = 2,00 , H/D = 4.00

CONTOUR I

VRLUE 0 -0500

2 3 4 5 6 7 8 9

O-tO00 0.I500 0,2000 0-2500 0.3144 0.3500 0,4000 0,4000

_•s . t.o

ItmNSVERSE omT. z/s

10

0,5000

-. . 1, ,o Te_V[_SE ols'[ _s

NEPSUREO THETR CONTOURS FOR TEST N0,34, TNRIN:CONST, J:26,4. S/D:2.0. H/O:4,0

Figure 79

138
CONTOUR I

VRLWE0.0500

_I_VElSE D S _

2 _ 4 5 6 7 8 9

O,IO00 0.1500 0.2000 0.2500 0,3144 0.3500 0.4000 0.4500

I0

0.5000

-0.5 V . .W L.O

PREDICTED THETR CONTOURS FOR TEST NO,B4, TNRIN=CONST, J=26.4, 5/0=2,0, H/0=4.0

s/oJ = 2,56

x/H = o,so x/od _,56

5-

/

ITMQIN-TJlITMRLN-TJ]

VRATIO = 3,44 TRRTIO = 0,4fl6 DENRRIIO=2,225

X/H = 0.75 XlOd _.84

5

(TNRIN-III(TMnlN-TJ)

TMR|N = 650,8 K TJET = _96,9 K THE8 = 0.314

X/H = 1,00 X/OJ =K,l_

o_ ,_ o_ l_ _ L_

_TNOIN_T J/_TN£IN_TJJ

COHPRRISON BETWEEN ORTR RNO CORRELRTION5 FOR TEST NO. 34, TEST SECTION VI,UNIFORM TMRIN. J = 26.40 , S/O =2,00 , H/D -4.00

Figure 80

139
8=0.0508 METERS 810J =4.961HOIDJ =9.921VMRIN =18.7MISECVJET =70.£MIBECTMA[N =561.4KTJET - 307,S K TREO = 0.1002 BLORAT= 8.£77

NERSUREO THETA PROFILES FOR TEST NO. 35, TEST SECTION V, TOP COLD , J =26.82 , S/D = 4.00 , HID = 8.00

T_f_SVeSE e[sT z/s

CONTOUR l

VRLUE 0.0500

2 3 4 5 6 7 8 £ tO 1[

O.tO02 0.1500 0.2000 0.2500 0,3000 0.3500 0.4000 0,5000 0,6000 0.7000

MEASUREO THETR CONTOURS FOR TEST N0.35, TOP COLD, J=26.82, 5/D=4.0, HID=8.0

Figure 81

140
_o.o

TP_NSVEe_EOiST, Ue

CONTOUR

VRLUE

t 2 3 4 5 6 ? 8 9

0,0500 0,I002 O,t500 0.2000 0,2500 0,3000 0,3500 0,4000 0.5000

°°

-o, 1.s i.o

6 Te_SVE_SE ozer, ZlS

PREDICTED THETA CONTOURS FOR TEST NO. 35, TOP COLD, J=26.82, S/D=4,0 HID=8.0

10

0.6000

ll

0,7000

$1OJ : 4,98

X/H = 0,25 X/OJ _,48

(TMRXITilITMRX-TJ)

VRRTIO = 3-79 TRRTIO = 0.548 OENRRTIO:t,864 TMRIN = 561.4 K TJET = 307,6 K

X/H = t,OO XlOd _.92

°.® 0.= o._ 0.® o_ ,.®

(TMAX-T]/[TMAX-TJ)

COMP£RISON BETNEEN OATR RND CORRELRTIONS FOR TEST NO I _5, TEST SECTION V, TOP COLD , d = 26,82 , 5/0 =4,00 , H/D =8,00

Figure 82

141
S =0.O508 METER8 8/OJ = 5.163 HO/OJ = 10.327 VMRtN = 18.8 VI/SEC V JET = 139.1 M/SEC TMAIN = 568.2 K TJET = 305.2 K TNEB = 0.17_ 8LORAT= 14.583

&--)p;....

MEASURED THETR PROFILES FOR TEST NO. 36. TEST SECTION V, TOP COLD • J = 109.80 , S/O = 4.00 , H/O = 8.DO

TRATIO=0.537

-o, mqNSVE_E Oral. Z/S . _.o

CONTOUR I 2 3 4 5 6 7 8 9 I0 II

VRLUE 0.0500 0.1000 0.1500 0.1768 0.2500 0.3000 0.3500 0.4000 0.5000 0.6000 0.7000

-m .

_v_sE olsl. _'s

MERSUREO THETR CONTOURS FOR TEST N0.36, TOP COLD, d=109.8, S/0=4.0, H/O:8.O

Figure 83

142
l.e

CONTOUR VALUEt 2 3 4 5 6 7 O 9 I0 tl

0-0500 0.I000 0.1500 0.1768 0.2500 0.3000 0.3500 0.4000 0.5000 0.6000 0.7000

_ oo

TR_ISVEe_ resT, _s

PREDICTED THETIq CONTOURS FOR TEST NO. 36, TOP COLD, J=109.8, S/D=4.0 H/D=8.0

S/DJ :

X/H = O.2B X/OJ_.SB

./

o._ o._ o._ o.® o.® ,.®

{TMRX-T]/ETMAX-TJ;

VRATIO = 7.39 TRATIO = 0.537 OENRRTIO=Z.OI2 TMAIN = 568.2 K TJET = 305-2 K THEB = O.tOt

XIH = 1.00 XlOJ =t0.33

o.= ,._ o.=

i

o.® o_ o.. °.® ,,. ,.®

(TRRX-T]/(TMAX-TJ]

COMPARISON BETNEEN DATA AND CORRELATIONS FOR TEST NO. 36, TEST SECTION V, TOP COLD ,

J = 109.80 . S/D =4.00 , H/D =8.00

Figure 84

143
S =0.0508 METERS S/DJ = 4,898 HO/DJ = 9.396 VMAIN = 16,0 N/SEC VJET = 40,7 M/SEC TMSIN = 417.3 R TJET = 3t9.0 K THEB = 0.0641 BLORAT= 3.850

MERSURED THETR PROFILES FOR TEST NO. 37, TEST SECTION V, TOP HOT , J = 8.51 , S/D = 4.00 , H/O = 8.00

_ ,j ,, i

II_VF_SE OlSI, Z/S

CONTOUR

VALUE

[ 2 3 4 5 6 7 B 9 10

0.0500 0,0041 0,I500 0-2000 0.2500 0-0000 0.3500 0,4000 0,5000 0,6000

TR_R_DIST, z/s

HERSUREO THETA CONTOURS FOR TEST N0.37, TOP HOT, J=8.gt, S/_=4.0, H/D=8.0

tt

0.7000

Figure 85

144
CONTOUR

V@LUE

1 2 3 4 6 6 7 8 9

0.0500 0.0641 0,1500 0.2000 0.2500 O,3GOO 0.3500 0,4000 0,5000

-o, T_R_ DIST, Z/S I.S

PREUICTEB THEm CONTOURS FOR TEST NO. 37, TOP HOT, J=8.S1, 8/0=4.0 H/0=8.0

tO

0.6000

ii

0.7000

8/OJ =

X/H = O.Z5 XlDJ _.35

9= 9_ oi®

o_ 0._ 0.. 0._ °.m ,,®

(TMRX-T)/(THRX-TJ]

VR@TIO = 2,54 TRRTIO = D.764 DENRRTIO= t .316 TMOIN = 417.3 _( TJET = 319.0 K

X/H = 1 .DO X/DJ _.40

0_ o_ o,_

[TMRX-T)/(TMRX-TJ)

CONPRRISON BETNEEN ORT8 8ND CORRELRTIONS FOR TEST NO. 37. TEST SECTION V, TOP HOT . J : 8.51 • S/O :4.00 , HID -8.00

Figure 86

145
S = 8.0508 METERS S/OJ = 4.925 HO/OJ = 9.851 VMRIN = 16.0 M/SEC VJET = 75.4 MISEC TMAIN = 416.l K fJEf = 314.5 R THEB = 0.t067 BLOR,qT= 7.163

MEASURED THETR PROFILES FOR TEST NO. 38, TEST SECTION V, TOP HOT , d = 30.24 , S/D = 4.00 , H/D = 8.00

n_A_SWSE OIST Z/S 1

CONTOUR 1

VRLUE 0.0500

2 3 4 5 0 7 8 9 tO 11

0-1067 0.t500 0.2000 0.2500 0-3000 0.3500 0.4000 0.5000 0.6000 0-7000

ilERSURED THETA CONTOURS FOR TEST NO.3B, TOP HOT, J=30.24, S/D=4.0, H/B=8.0

Figure 87

146
CBNTOUR

VRLUE

1 2 3 4 5 6 7 8 9 10 11

O,05GO 0,1007 0-1500 0,2000 0.25G0 0.3000 0.3500 0-4000 0.5000 0.0000 0-7000

PREDICTED THETFI CONTOURS FOR TEST NO. 38, TOP HOT, J=30.24, SID=4.0 H/0=8.0

s/oJ = 4.93

X/H - O.Z5 X/DJ _.46

!

(TMRX-T)/(TMRX-TJ)

VR£TIO = 4mq2 TRAT[O 01756 OENRnTIO=I.356 TMAIN = 418.1K TJET = 314.5 K THEB r 0m023

X/H = 1,00 X/OJ_.B5

I °'-"

{TNRX-T)/(TMRXITj)

CONPRRISON BETWEEN OATR AND CORRELRTIONS FOR TEST NO. 38, TEST SECTION V, TOP HOT , J = 30.24 , S/D =4.00 , H/D =8.00

Figure 88

147
APPENDIX A

LIST OF SYMBOLS

A test section cross-sectional area at survey plane

D geometric orifice diameter

O ,

3

H

o

H

J

P

t

P

s

effective orifice diameter

duct height at the jet injection plane

local duct height at the survey plane

momentum ratio (PjVj2)/_mVm 2)

stagnation pressure

static pressure

orifice spacing

T temperature

V

X

velocity

X direction, parallel to duct axis

Y y direction, parallel to orifice centerline (radial direction)

Z Z direction, normal to duct axis (transverse direction)

Greek

temperature difference ratio

P density

jet injection angle

Subscripts

av

EB

J

max

m

average

equilibrium value

jet property

maximum

cross-flow property, average value

148
APPENDIXB

REFERENCES

l. Holdeman, J. D., R. E. Walker, and D. L. Kors, "Mixing of

Multiple Dilution Jets with a Hot Primary Airstream for Gas

Turbine Combustors," AIAA Paper 73-1249, Las Vegas, Nevada

1973 (also NASA TM X-71426).

. Holdeman, J. D., and R. E. Walker, "Mixing of a Row of Jets

with a Confined Cross-flow," AIAA Journal, Vol. 15, No. 2,

Feb. 1977, pp 243-249.

• Walker, R. E., and D. L. Kors, "Multiple Jet Study, Final

Report," NASA CR 121217.

Walker, R. E., and R. G. Eberhardt, "Multiple Jet Study Data

Correlations," NASA CR-134795, 1975.

0 Kamotani, Y., and I. Greber, "Experiments on a Turbulent Jet

in a Cross-Flow," AIAA Paper 72-149•

6. Ricou, R. P., and D. B. Spalding, "Measurements of Entrainment by Axisymmetrical Turbulent Jets," Journal of Fluid

Mechanics II, 25-32 (1961).

7. Kamotani, Y., and I. Greber, "Experiments on Confined Turbulent Jets in Cross-flow," NASA CR-2392 (1974).

8. McAllister, J. D., "A Momentum Theory for the Effects of

Cross-flow on Incompressible Turbulent Jets," Ph.D. Thesis

(University of Tennessee, 1968).

9. Abram.rich, G. N., The Theory of Turbulent Jets, Cambridge,

Massachusetts, MIT Press, 1963.

i0. Keffer, J. F., and W. D. Baines, "The Round Turbulent Jet in

a Cross-Wind," J. Fluid Mech. 15, 481-496 (April 1963).

ii. Stoy, R. L., and Y. Ben-Haim, "Turbulent Jets in a Confined

Cross-Flow," J. Fluids Eng. 95, 551-556 (December, 1973).

12. Sucec, J., and W. W. Bowley, "Prediction of the Trajectory of

a Turbulent Jet Injection into Cross-Flowing Stream,"

J. Fluids Eng. 98, 667-673 (December 1976).

149
Form Approved REPORT DOCUMENTATION PAGE

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

November 1982 Final Contractor Report

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Dilution Jet Mixing Phase I Program

6. AUTHOR(S)

R. Srinivasan, A. Berenfeld, and H.C. Mongia

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Garrett Turbine Engine Company

A Division of the Garrett Corporation

Phoenix, Arizona 85010

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

DlJ-None

NAS3-22110

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REPORT NUMBER

E-None

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA CR-168031

Garrett 21-4302

11. SUPPLEMENTARY NOTES

Project Manager, James D. Holdeman, NASA Lewis Research Center, Cleveland, Ohio 44135.

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Unclassified - Unlimited

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Available electronically at http://gltrs.grc.nasa.gov

This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The main objective of the NASA Dilution Jet Mixing Phase I Program was to quantify by means of parametric tests the

effect of the following on the mixing of a row of jets with a confined cross-flow. 1) Jet to mainstream density ratio;

2) Flow area convergence as encountered in transition sections; and 3) Non-uniform mainstream profile upstream of

dilution orifices. The general conclusions derived from Phase I work are: 1) Jet spreading rate in transverse direction is

increased with increasing J, H/D and with decreasing S/D; 2) The density ratio has only a second order effect on the jet

mixing characteristics for a constant momentum ratio; 3) The temperature distributions in the jet mixing region are

strongly influenced by the undisturbed mainstream profile. Therefore, a superposition of the mainstream profile on the

correlations for isothermal mainstream conditions yields good agreement with data; and 4) Flow area convergence

enhances mixing in radial and transverse directions. An asymmetric convergent duct with flat wall injection has the same

jet mixing characteristics as a symmetric convergent duct. An asymmetric convergent duct with slant wall injection has a

faster jet spreading rate in the transverse direction.

14. SUBJECT TERMS

Dilution-zone; Jet-mixing; Combustion

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